Bibliography on the evaluation of numerical software Science Division and Electronics Research ......

BIBLIOGRAPHY 010

Bibliography on the evaluation of numerical software

Bo Einarsson (*)

ABSTRACT

This bibl iography on the evaluation o f numerical sof tware has been wri t ten at the request o f the IFIP Working Group on Numerical Software (IF1P WG 2.5), and is divided into nine different sections. Within each section the references are given in alphabetical order by the first author .

The aim o f the bibl iography is to be useful in the p roduc t ion and evaluation o f good software for numerical mathemat ics .

HISTORY OF THIS BIBLIOGRAPHY

A first bibliography on numerical software, with the title "An Annotated Bibliography on Mathematical Software and Related Topics", was written in 1974 by Eva Edberg and Jan Johansson and was later published in the SIGNUM Newsletter, Vol. 11, No. 2 (August 1976), pp. 9-16, and No. 3 (October 1976), p. 6. At the request of the IFIP Working Group on Numer- ical Software (IFIP WG 2.5) I started early in 1975 to collect additional material, and in March 1977 the report "Bibliography on Numerical Software", Memo- randum No. UCB/ERL M77/19, was produced at the Computer Science Division and Electronics Research Laboratory, University of California, Berkeley, Califor- nia. This report is now out of print but available as R77-231 with 123 pages from the IEEE Repository, IEEE Computer Society, 5855 Naples Plaza, Suite 301, Long Beach, California 90803, and as AD-A038827/ 2GA from the National Technical Information Service, Spdngfleld, Virginia 22161. The previous report was divided into twenty-one different areas, while the present bibliography is an up- dated version of area 16 (Evaluations) in that report.

My work on the Berkeley version was supported by grants from the Sweden-America Foundation and the National Science Foundation, while the production was financed by the Office of Naval Research. I wish to express my sincere thanks to these three organiza- tions for their support and to the Swedish National Defence Research Institute for supporting the present revision.

SUBDIVISIONS OF THE BIBLIOGRAPHY

1. General Articles 2. Miscellaneous Evaluations 3. Linear Algebra 4. Optimization and Nonlinear Equations 5. Functions 6. Quadrature 7. Integral Equations 8. Ordinary Differential Equations 9. Partial Differential Equations

ACKNOWLEDGEMENTS

I would like to thank Eva Edberg and Jan Johansson for their excellent original work. I also thank Ed. L. Battiste, Richard Brent, W. Stanley Brown, William J. Cody, Fred N. Fritsch, Thos. E. Hull, Tapio Niemel/i, John R. Rice, Klaus Schittkowski, and Larry F. Shampine for significant contributions.

(*) Bo Einarsson, FORSVARETS F O R S K N I N G S A N S T A L T (FOA), National Defence Research Institute, Depa r tmen t 2/Proving Grounds, Box 98, S-147 00 Tumba, Sweden.

Journal of Computational and Applied Mathematics, vohme 5, no 2, 1979. 145

BIBLIOGRAPHY

I. GENERAL ARTICLES

1.01 AMSTER, S J; DICKMAN, B N (1976): An Experiment in Automatic Quality Evaluation of Software, In Proceedings of the "Polytechnic Institute of New York - MRI Symposium on Computer Software Engineering", 20-22 April 1976. Volume XXIV of ERI Symposia Series, Polytechnic Institute of New York, MRI Symposium Committee, 333 Jay Street, Brooklyn, New York 11201.

1.02 BAILEY, Carl B; JONES, Rondall E (1975): Usage and Argument Monitoring of Mathematical Library Routines, ACM Transactions on Mathematical Software, Vol. I, pp. 196-209.

1.03 BARTH, Jeffrey M (1978): A Practical Interprocedural Data Flow Analysis Algorithm, Communications of the ACM, Vol. 21, pp. 724-736.

1.04 BATE, Roger R; LIGLER, George T (1978): An Approach to Software Testing: Methodology and Tools, Proceedings of COMFSAC78, The IEEE Computer Society's Second International Computer Software & Applications Conference, IEEE Catalog No. 78CH1338-30, pp. 476-480.

1.05 BRIGHT, H S; COLE, I J (1973): A method of testing programs for data sensitivity, In HETZEL, William C (Ed.): Program Test Methods, Prentice-Hall, Englewood Cliffs, pp. 143-162.

1.06 BROWN, J R; HOFFMAN, R H (1972): Evaluating the effegtlveness of software verification - practical experience with an automated tool, In Proceedings of AFIPS, VOI 41, P a r t I, Fall J o i n t Computer Conference, pp. 181-190.

1.07 BROWN, W Stanley (1979): Some fundamentals of performance evaluation for numerical software, in "Performance Evaluation of Numerical Software", Proceedings of the IFIF TC 2 Working Conference held in Baden, Austria, 11-15 December 1978, edited by Lloyd D. Fosdick, to be published by North-Holland, Amsterdam.

1.08 CHEN, Wen-Tsuen; He, Jone-Ping; WEN, Chia-Hsien (1978): Dynamic Validation of Programs Using Assertion Checking Facilities, Proceedings of COMPSAC78, The IEEE Computer Society's Second International Computer Software & Applications Conference, IEEE Catalog No. 78CH1338-3C, pp. 533-538.

1.09 CLARKE, Lori A (1976): A System to Generate Test Data and Symbolically Execute Programs, IEEE Transactions on Software Engineering, Vol. SE-2, pp. 215-222.

1.10 CLARKE, Lori A (1978): Testing: Achievements and Frustrations, Proceedings of C0M~BAO78, The IEEE Computer Society's Second International Compeer Software & Applications Conference, IEEE Catalog No. 78CH1338-3C, pp. 310-314.

1.11 CODY, W J (1973): The Evaluation of Ra~hamatioal Software, In HETZEL, William C (Ed.): Program Test Methods, Prentice-Ball, Englewood Cliffs, pp. 121-133.

1.12 CODY, W J (1974): The ConsCruotion of Numerical Subroutine Libraries, SIAM Review, Vol. 16, pp. 36-46.

1.13 CODT, W J (1976): Mathematical Software - Why the Fuss, Presented at the SIAM 1976 National Meeting, 16-18 June, Chicago, Illinois. Abstract in SIAM Review, Vol. 19 (1977), p. 378.

1.1h COHEN, Jacques; CARPENTER, Neal (1977): A Language for Inquiring about the Run-time Behaviour of Programs, Software - Practice and Experience, Vol. 7, pp. 445-460.

1.15 COWELL, Wayne R (Editor) (1972): Proceedings of the Software Certification Workshop, Snow Mountain Ranch, Oranby, Colorado, 27-30 August 1972.

1.16 COWELL, Wayne R (1977): The Validation of Mathematical Software, In "Selected Topics in Information Processing IFIP-INFOFOL-1976", Proceedings of the International IFIP/INFOFOL Conference, Warsaw, Poland, March 22-27, 1976. Edited by Jan Madey, North-Holland Publishing Company, Amsterdam, 534 pp.

1.17 COWELL, W R; FOSDICK, L D (1977): Mathematical Software Production, In "Mathematical Software III", edited by John R. Rice, Academic Press, New York, pp. 195-224.

1.18 CROWDER, R P; DE~O, R S; MULVEY, J M (1979): On Reporting Computational Experiments with Mathematical Software, ACM Transactions on Mathematical Software, Vol. 5, to appear.

1.19 DEKKER, Theodorus J (1979): Correctness proof and machine arithmetic, in "Performance Evaluation of Numerical Software", Proceedings of the IFIP TC 2 Working Conference held in Baden, Austria, 11-15 December 1978, edited by Lloyd D. Fcsdick, to he published by North-Holland, Amsterdam.

1.20 EINARSSON, Be 41974): Utv~rdering av matematisk programvara - En komhinaticn av matematik, numerisk analys, datalogi ooh informationsteknik (in Swedish, Evaluation of mathematical software- A combination of mathematics, numerical analysis, computer science and library science). ITM Working paper no. 19, Swedish Institute of Applied Mathematics, Stockholm, Sweden. Lecture at Chalmers University of Technology.

1.21 EINABSSON, Be (1977): The Applicability of Data Flow Anaiysis t o Different Programming Languages, FOA Report C 20209-M4, Ftrsvarets Forskningsanstalt, Stockholm, SWeden.

1.22 EINARSSON, Be (1977): Solving a System of Linear Inequalities for Generating Test Data, Journal of Computational and Applied Mathematics, Vol. 3, PP. 269-271.

1.23 FAIRLEY, Richard E (1975): An Experimental Program Testing Facility, IEEE Transactions on Software Engineering, Vol. SE-I, pp. 350-357.

I~2h FITZSIMMONS, Ann; LOVE, Tom (1978): A Review and Evaluation of Software Science, Computing Surveys, Vol. 10, pp. 3-18.

1.25 FORD, Brian (1976): Some Transformations of Numerical Software, Presented at the SIAM 1976 National Meetihg, 16-18 June, Chicago, Illinois. Abstract in SIAM Review, Vol. 19 (1977), p. 381~

~.26 FORD, Brian; HODOSON, Graham S; SAYERS, David K (1979): Evaluation of numerical software for many machines - is it possible? in "Performance Evaluation of Numerical Software", Proceedings of the IFIP TC 2 Working Conference held in Baden, Austria, 11-15 December 1978, edited by Lloyd D. Fosdick, to be published by North-Holland, Amsterdam.

1.27 FORSYTHE, George E; MALCOLM, Michael A; MOLER, Cleve B (1977): Computer Methods for Mathematical Computations, Prentice-Hall, Englewood Cliffs, New J e r s e y , 259 pp.

1.28 FO~DIOK, Lloyd D; OSTERWEIL, Leon J (1975): DAVE - A FORTRAN program a n a l y s i s system, In "P roceed ings o f computer science and statlstios: 8th annual symposium on the interface", (University of California, Los Angeles, 13-14 February 1975), James W. Frane (Editor), Health Sciences Computing Facility, Los Angeles, California, pp. 329-335.

1.29 FOSDICK, Lloyd D; OSTERWEIL, Leon J (1976): Data Flow Analysis in Software Reliability, Computing Surveys, Vol. 8, pp. 305-330.

1.30 FOSDICK, Lloyd D; OSTERWEIL, Leon J (1976): The Detection of Anomalous Interprooedural Data Flow, Technical Report No. CU-CS-090-76, Department of Computer Science, University of Colorado, Boulder, Colorado 80309.

1.3i FOSDIOK, Lloyd D (1979): Detecting errors in software, in "Performance Evaluation of Numerical Software", Proceedings of the IFIP TC 2 Working Conference held in Baden, Austria, 11-15 December 1978, edited by Lloyd D. Fosdick, to be published by North-Holland, Amsterdam.

1.32 FOX, P A; HALL, A D; SCHRYER, N L (1978): The PORT Mathematical Subroutine Library, ACM Transactions on Mathematical Software, Vol. 4, pp. 104-126.

1.33 FRANCIS, I; HEIBEROER, P M; VELLEMAN, P F (1975): Criteria and Considerations in the Evaluation of Statistical Program Packages, Amer. Station., Vol. 29, pp. 52-56.

Journal of Computational and Applied Mathematics, volume 5, no 2, 1979. 146

1.3~ FRANCIS, I (1975): DesiEn for Evaluation of Statistical Program Packages, Bull. Intl. Stat. Inst., Col. 46, pp. 573-584.

1.35 GARY, John M (1977): Analysis of Applications Programs and Software Requirements for High Speed Computers, In "High Speed Computer and Algorithm Organization", edited by David J. Kuck, Duncan H. Lawrie, and Ahmed H. Sameh, Academic Press, New York 1977, pp. 329-354.

1.36 GELLER, Matthew (1978): Test Data as an Aid in Proving Program Correctness, Communications of the ACM, Vol. 21, pp. 368-375.

1.37 GEPNEE, Herbert L (1978): User ratings of software packages, Datamation, December 1978, pp. 163-227.

1.38 GILB, Tom (1977): Software Metrics, Winthrop l~blishers, Cambridge, Massaqhuaetta.

1.39 GINSBERG, M (197Z): A Review of Superoomputers for Scientific Computation, Presented at the SIGNUM Meeting on Mathematical Software, 3-4 November 1977, Albuquerque, New Mexico. Abstract in the SIGNUM Newsletter, Vol. 12, No. 4 (December 1977), p. 8.

1.h0 GINSEERG, Myron (1977): Numerical influences on the design of floating-point arithmetic for microcomputers, Proceedings let Annual Rocky Mountain Symposiu~ on Microcomputers, IEEE Computer Society, pp. 24-72.

1.h l GOODENOHGH, J B (1977) : A s u r v e y o f p rog ram t e s t i n g issues, in "Software Reliability", edited by R. K. D. Rees, Infotech International Ltd., Maidenhead, Berkshire, P a r t 2, pp. 135-154.

1.42 HALSTEAD, Maurice H (1977): Elements of Software Science, Operating and Programming Systems Series, Elsevier Computer Science Library, Elsevier, New York-Crxford-Amsterdam, 127 pp.

1.43 HA~ER, C (1967): Statistical validation of mathematical computer routines, AFIPS Conference Proceedings, Spring Joint Computer Conference, pp. 311-333.

I.h4 HEATH, M T; FUNDEELIC, R E (1978): The Organization of Our Numerical Software Library (Union Carbide corporation, Oak Ridge), Presented at the SIAM 1978 Fall Meeting, October 30 - November I, Knoxville, Tennessee.

I.~5 HEIBERGER, Richard M (1975): A Procedure for the Review of Statistical Packages and its Application t o the User Interface with Regrsssio~ Programs, In the Proceedings of "Computer Science and Statistics: 8th Annual Symposium on the Interface", pp. 115-121.

I.~6 HENNELL, M A (1978): An experimental testbed for numerical software, The Computer Journal, Vol. 21, pp. 333-336.

1.47 HETZEL, Wi l l i am C (1973) : P r i n c i p l e s o f computer p rogram t e s t i n g , In HETZEL, Wi l l i am C ( E d . ) : Program Tes t Methods, P r e n t i c e - H a l l , Englewood C l i f T s , pp . 17-28 .

1.~8 HOAGLIH, David C (1977) : M a t h e m a t i c a l S o f t w a r e and Exploratory Data Analysis, In "Mathematical Software III", edited by John R. Rice, Academic Press, New York, pp. 139-159.

I.~9 EOWDEN, William E (1978): Theoretical and Empirical Studies of Program Testing, IEEE Transactions on Software Engineering, Vol. SE-4, pp. 293-298.

1.50 HULL, Tom E (1979): Correctness of numerical software, in "Performance Evaluation of Numerical Software", Proceedings of the IFIP TC 2 Working conference held in Baden, Austria, 11-15 December 1978, edited by Lloyd D. Fosdiok, to be published by North-Holland, Amsterdam.

1.51 HOYT, Patrick M (1977): The Navy Fortran Validation System, In AFIPS Conference Proceedlngs, Vol. 46, National Computer Conference 13-16 June 1977, Dallas, Texas, pp. 529-537.

1.52 IVIE, Evan L (1977): The Programmer's Workbench - A Machine for Software Development I Commenications of the ACM, Vol. 20, pp. 746-753.

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Journal of Computational and Applied Mathematics, volume

1.53 KING, James C (1978): Prospects for Program Verification, Tutorial Session, Proceedings of the Third International Conference on Software Engineering, 10-12 May 1978, Atlanta, Georgia. IEEE Catalog No. 78CH1317-7C, p. 71.

1.5~ KNUTH, D E (1971): An Empirical Study of FORTRAN Programs, Software - Practice and Experience, Vol. I, pp. I05-133.

1.55 KEOGH, Fred T (1971): A Plea for Tolerance in the Evaluation of Numerical Methods and Mathematical Software. SIGNUM Newsletter, Vol. 6, No. 3, PP. 7-8, November 1971.

1.56 LIM, R T C; BLACKBURN, J D (1976): On Program Verification in Numerical Methods, Letter to the Editor, The Computer Journal, Vol. 19, pp. 272-273.

1.57 LYNESS, James (1979): Performance profile and software evaluation, in "Performance Evaluation of Numerical Software", Proceedings of the IFIP TC 2 Working Conference held in Baden, Austria, 11-15 December 1978, edited by Lloyd D. Fosdick, to be published by North-Holland, Amsterdam.

1.58 MILLER, E F (1975): RXVP: An automated verification system for FORTRAN, In " Proceedings of computer science and statistics: 8th annual symposium on the interface, (University of California, Los Angeles, 13-14 February 1975), James W. Frane (Editor), Health Sciences Computing Facility, LOS Angeles, California, p. 328.

1.59 MILLER, Edward F (1977): Program Testing Teshniquas, Tutorial, IEEE Catalog No. EHO 130-5, 289 pp. New edition together with William E. Howdah with the title "Software Testing and Validation Techniques", 428 pp., 1978.

1.60 MILLER, Edward F (1978): Special Issue on Program Testing of the IEEE Computer, Vol. 11, No. 4, pp. 10-60 .

1.61 MILLER, Edward F (1978) : Program T e s t i n g - An Overview for Managers, Proceedings of COMPSAC78, The IEEE Computer Society's Second International Computer Software & Applications Conference, IEEE Catalog No. 78CH1338-3C , pp. 114-119.

1.62 MILLER, Webb C; SPOONER, David (1976): Automatic Generation of Floating-Polnt Test Data, IEEE Transactions on Software Engineering, Vol. SE-2, pp. 223-226.

1.63 MILLS, H D (1970): On the statistical validation of computer p r o g r a m s , IBM Repor t FSC-72-6015, 16 pp.

1.64 MOEANTY, S N (1976): Proposed Measures for Evaluation of Software, In Proceedings of the ,Polytechnic Institute of New York - MEI Symposium on Computer Software EnEineering", 20-22 April 1976. Volume XXIV of MRI Symposia Series, Polytechnic Institute of New York, MRI Symposium Committee, 333 Jay Street, Brooklyn, New York 11201.

1.65 NELDER, J A (1979): Experimental design and statistical evaluation, in ",Performance Evaluation of Numerical Software", ~roceedings of the IFIP TC 2 Working Conference held in Baden, Austria, 11-15 December 1978, edited by Lloyd D. Fosdiek, to be ~ublished by North-Holla~d, Amsterdam.

1.66 NG, E W (1973): Mathematical Software Testing Activities, In HETZEL, William C (Ed.): Program Test Methods, Prentice-Hall, Englewood Cliffs, pP. 135-1ql.

1.67 OSTEEWEIL, Leon; FOSDICE, Lloyd D (1974): Automated Input~Output Variable Classification as an Aid to Validation of Fortran Programs, Technical Report No. CU-CS-037-7% Department of Computer Science, University of Colorado, Boulder, Colorado 80309.

1.68 OSTERWEIL, Leon (1975): Depth-First Search Techniques and Efficient Methods for Creating Test Paths, Technical Report No. CU-CS-077-75, Depar tment of Computer Science, University of Colorado, Boulder, Colorado 80309.

1.69 OSTERWEIL, Leon J; FOSDICK, Lloyd D (1976): Some Experience with DAVE -- A Fortran Program Analyzer, Technical Report No. CH-CS-088-76, Department of Computer Science, University of Colorado, Boulder, Colorado 80309.

5, no 2, 1979. i47

1.70 OSTERWEIL, Leon d (1976): A Proposal f o r an Integrated Testing System for Computer Programs, Technical Report No. CU-CS-093-76, Department of Computer Science, University of Colorado, Boulder, Colorado 80309.

1.71 OSTERWEIL, Leon J; FOSDICK, Lloyd D (1976): DAVE - A Validation, Error Detection, and Documentation System for Fortran Programs. Software - Practice and Experience, Vol. 6, pp. 473-486.

1.72 PAIGE, Michael R (1978): An Analytical Approach to Software Testing, Proceedings of COMPSAC78, The IEEE Computer Society's Second International Computer Software & Applications Conference, IEEE Catalog No. 78CH1338-3C, pp. 527-532.

1.73 PARLETT, Beresford (1978): Progress in Numerical Analysis, SIAM Review, Vol. 20, pp. 443£456.

1.7h RICE, John R (1976): TOMS Policy Statement, The Rights of Program Authors in the Evaluation of Programs, ACM Transactions on Mathemstioal Software, Vol. 2, pp. 113-114.

1.75 RICE, John R (1976): The algorithm selection problem, In "Advances in Computers", Vol. 15, Edited by M. Rubincff and M. C. Yoritz, Academic Press, New York 1976, pp. 65-118.

1.76 RICE, John R (1978): Software for Numerical Computation, in "Research Directions in Software Technology", MIT press, p. I.

1.77 RICE, John R (1979): Methodology for the algorithm selection problem, in "Performance Evaluation of Numerical Software", Proceedings of the IFIP TC 2 Working Conference held in Baden, Austria, 11-15 December 1978, edited by Lloyd D. Fosdick, to he published by North-Holland, Amsterdam.

1.78 RICHARDS, F R (1974): Computer Software: Testing, Reliability Models, and Quality Assu?anee. Monterey Naval Postgraduate School, 80 pp.

1.79 ROSEN, B a r r y K (1977): High-Level Data Flow Analysis, Communications of the ACM, Vol. 20, pp. 712-724.

1.80 SAMEH, Ahmed H (1977): Numerical Parallel Algorithms - A Survey, In "High Speed Computer and Algorithm Organization", edited by David J. Kuek, Duncan H. Lawrie, and Ahmed H. Sameh, Academic Press, New York 1977, pp. 207-228.

1.81 SCHAEFER, Marvin (1973): A Mathematical Theory of Global Program Optimization, Prentice-Hall, Englewood Cliffs, New Jersey, 198 pp.

1.82 STETTER, Hans J (1976): Aspects of Man-Software Communication, Presented at the SIAM 1976 National Meeting, 16-18 June, Chicago, Illinois. Abstract in SIAM Review, Vol. 19 (1977), p. 398.

1.83 TAYLOR, Richard N; OSTERWEIL, Leon J (1978): A Facility for Verification, Testing and Documentation of Concurrent Process Software, Proceedings of COMPSAC78, The IEEE Computer Society's-second International Computer Software & Applications Conference, IEEE Catalog No. 78CH1338-3C, pp. 36-41.

1.8~ USOW, Karl H (1969): Certification Bibliography, SIGNL~4 Newsletter, Vol. 4, "No. 3, October 1969, pp. 16-18, and Vol. 5, No. 2, August 1970, pp. 1~-15.

1.85 USOW, Karl H; FOSDICK, Lloyd D (1969): Guidelines for Evaluating an Algorithm for Publication, SIGNUM Newsletter, Vol. 4, No. 3, October 1969, pp. 19-20.

1.86 VOIGT, R o b e r t G (1977): The Influence of Vector Computer Architecture on Numerical Algorithms, In "High Speed Computer and Algorithm Organization", edited by David J. Kuck, Duncan H. Lawrie, and Ahmed H. Sameh, Academic Press, New" York 1977, pp. 229-244.

1.87 WASSERMAN, Anthony I; BELADY, L A (1978): Software Engineering: The Turning Point, Computer (IEEE), Vol 11 (September 1978), pp. 30-41.

1.88 WEIDE, Bruce (1977): A Survey of Analysis Techniques for Discrete Algorithms, Computing Surveys, Vol. 9, pp. 291-313.

1.89 WEINBERG, G e r a l d M (1971): The Psychology of Computer Programming, Van Nostrand Reinhold, New York, 298 pp.

1.90 WIC~4ANN, B A (1973): Estimating the Execution Speed of an Algol Program, National Physical Laboratory, NPL Report NAC 38, June 1973.

1.91 WIRSCHING, J E; KISHI, T (1977): Matching Machines and Problems, In "High Speed Computer and Algorithm Organization", edited by David J. Kuck, Duncan H. Lawrie, and Ahmed H. Sameh, Academic Press, New York 1977, pp. 379-397.

2. MISCELLANEOUS EVALUATIONS

2.01 ANONYMOUS (1978): Sorting 30 Times Faster with DPS (Distributive Partitioning Sort), DATAMATION, February 1978, pp. 200-203.

2.02 ANONYMOUS (1978): Sort Scoop Settled (Editorial and letters by Zimmer, Dobosiewiez, and FerEuson), DATAMATION, August 1978, pp. 31 and 34.

• 2.03 ATKINSON, A C; PEARCE, M C (1976): The Computer Generation of Beta, Gamma and Normal Random Variables, J. Roy. Statist. See. A, Vol. 139, Part 4, pp. 431-461.

2.0~ BARINKA, L L; NEVES, K W; TUTTLE, P G (1975): Performance of Some Vectorized Mathematical Software, Presented at the SIAM-SIGNUM 1975 Fall Meeting, 3-5 December, San Francisco, California. Abstract in SIAM Review, Vol. 18 (1976), p. 794.

2.05 BANINKA, L L; CONNELLY, W H; THOMPSON, S; TUTTLE, P G (1976): Performance of Some Vectorized Mathematical Software, Part 2, Presented at the SIAM 1976 National Meeting, 16-18 June, Chicago, Illinois. Abstract in SIAM Review, Vol. 19 (1977), pp. 375-376.

2.06 de BOOR, Carl (1978): A Comment on "Numerical Comparisons of Algorithms for Polynomial and Rational Multivariate Approximations", SIAM Journal on Numerical Analysis, Vol. 15, pp. 1208-1211.

2.07 DOBOSIEWICZ, Woldzmierz (1978): Sorting by ~ Distributive partitioning, Information Processing Letters, Vol. 7, No. I (January 1978), pp. I-6.

2.08 FRANCIS, Ivor (1977): A Biblio~ahy for Statistical Software: Reviews, Evaluations, Standards and Improvements, Economic and Social Statistics Technical Report Series No. 1077/013, Cornell University, Ithaca, New York 14583.

2.09 FRANKE, Richard (1978): Comparison of Some Local Methods for Interpolation of Scattered Data, Presented at the SEAM 1978 Spring Meeting, 24-26 May 1978, Madison, Wisconsin.

2.10 GALANTAI, Aurel (1978): The Comparison of Numerical Methods for Solving Polynomial Equations, Mathematics of Computation, Vcl. 32, pp. 391-397.

2.11 GAUTSCHI, Walter (1977): Anomalous Convergence of a Continued Fraction for Ratios of gummer Functions, Mathematics of Computation, Vol. 31, PP. 994-999.

2.12 GINSBERG, Myron (1977): Some Numerical Effects of a FORTRAN Veotorizing Compiler on a Texas Instruments Advanced SelentlficComputer, In "High Speed Computer and Algorithm Organization", edited by David J. Kuck, Duncan H. Lawrie, and Ahmed H. Sameh, Academic Press, New York 1977, pP. 461-462.

2.13 GONNET, Gaston.H (1977): On the Structure of Zero Finders, BIT, Vol. 17, pp. 170-183.

2.1h HENRY, Jackson N (1977): Comparison of Algorithms for Multivariate Rational Approximation, Mathema$ies of Computation, Vol. 31, pp. 485-494.

2.15 HENRY, J N; HENRY, M S; SC~IDT, D (1978): Numerical Comparisons of Algorithms for Polynomial and Rational Multivariate Approximations, SIAM Journal o~ Numerical Analysis, Vol. 15, pp. 1197-1207.

2.16 HOWDEN, William E (1978): An Evaluation of the Effectiveness of Symbolic Testing, Software - Practice and Experience, Vol. 8, pp. 381-397.

2.17 JENKINS, M A; TRAUB, J F (1975): Principles for Testing Polynomial Zerofinding Prepares, ACM Transactions on Mathematical Software, Vol. I, pp. 26-34.


2.18 KUKI, H; CODY, W J (1973): A statistical study of the accuracy of floating point number systems, Communications of the ACM, Vol. 16, pp. 223-230.

2.19 LEECE, John; Parker, Frank (1978): Use and Misuse of SPSS, Software-Practlee and Experience, Vol. 8, pp. 301-311.

2.20 LOESER, R (1974): Some Performance Test of "quicksort" and Descendants, Communications of the ACM, Vol. 17, No. 3, pp. 143-152.

2.21 LOESER, Rudolf (1976): Survey on Algorithms 347, 426, and Quickscrt, ACM Transactions on Mathematical Software, Vol. 2, pp. 290-299.

2.22 MYERS, Glenford J (1978): A Controlled Experiment in Program Testing and Code Walkthroughs/Inspeotions, Communications of the ACM, Vol. 21, pp. 760-768.

~.23 PARKER, D Stott (1977): Nonlinear Recurrences and Parallel Computation, In "High Speed Computer and Algorithm Organization", edited by David J. Kuck, Duncan H. Lawrie, and Ahmed H. Sumeh, Academic Press, New York 1977, pp. 317-320.

2.2h PAYNE, W H (1977): Normal Random Numbers: Using Machine Analysis To Choose the Best Algorithm, ACM Transactions on Mathematical Software, Vol. 3, PP. 346-358.

2.25 REMUND, R N; TAGGART, K A (1977): To Vectorize or to "Vectorize": That is the Question, In "High Speed Computer and Algorithm Organization", edited by David J. Kuok, Duncan H. Lawrie, and Ahmed H. Sameh, Academic Press, New York 1977, pp. 399-410.

2.26 SLYSZ, W D (1974): An Evaluation of Statistical Software in the Social Sciences, Cc~nmunications of the ACM, Vol. 17, No. 6, pp. 326-332.

2.27 SPARKS, Paui R (1978): Sorting out sorting (letter), DATAMATION, May 1978, pp. 26,32,319.

2.28 STONE, Harold S (1978): Sorting on STAR, IEEE Transactions on Software Engineering, Vol. SE-4, pp.138-146.

2.29 TESSLER, Harvey B (1978): More on sorting (letter), DATAMATION, July 1978, p. 26.

3. LINEAR ALGEBRA

3.01 AXELSSON, Owe (1976): A class of iterative methods for finite element equations, Computer Methods in Applied Mechanics and EngineerlnE, Vol. 9, No. 2, pp. 123-137.

3.02 BARINKA, Lawrence L (1975): Some Experience with Constructing, Testing, and Certifying a Standard Mathematical Subroutine Library, ACM Transactions on Mathematical Software, Vol. I, pp. 165-177.

3.03 BARWELL, Victor; GEORGE, Alan (1976): A comparison of algorithms for solving symmetric indefinite systems of linear equations, ACM Transactions on Mathematical Software, Vol. 2, pp. 242-251.

3.04 BLASER, A; SCHAUER, H (197~): Performance Measurements on the Sparse Matrix Subroutines of S.L-Math, In "Mathematical Software II", Informal Proceedings of a Conference, edited by John R Rice. Purdue University, May 29-31, 1974, p. 301.

3.05 BUNCH, James H; KAUFMAN, Linda (1977): Some Stable Methods for Calculating Inertia and Solving Symmetric Linear Systems, Mathematics of Computation, Vol. 31, pp. 163-179.

3.06 CABAY, S; LAM, T P L (1977): Congruence Techniques for the Exact Solution of Integer Systems of Linear Equations, ACM Transactions on Mathematical Software, Vol. 3, pp. 386-397.

3.07 CHAN, Chorkln; KLASSEN, Melvin (1975): A performance comparison study between subroutine packages LINSYS, IBMSSP and IMSL for solving systems of linear equations, Journal of Computational and Applied Mathematics, Vol. I, No. 2, pp. 111-113.

3.08 CHEN, S C; KUCK, D J; SAMEH, A H (1978): Practical Parallel Band Triangular System Solvers, ACM Transactions on Mathematical Software, Vol. 4, pp. 27O-277.

3.09 CLINE, A K; MOLER, C B; STEWART, G W; WILKINSON, J H (1977): An Estimate for the Condition Number of a Matrix, LINPACK Working Note No. 7, Technical Memorandum No. 310, Applied Mathematics Division, Argonne National Laboratory, Argonne, Illinois 60439.

3.10 CONCHS, P; GOLUB, G H; O'LEARY, D P (1978): Numerical Solution of Nonlinear Elliptic Partial Differential Equations by a Generalized Conjugate Gradient Method, Computing, Vol. 19, pp. 321-339.

3~11 DEMBAR~ B; NEVES, K W (1977): sparse Triangular Faetorization on Vector Computers, 3-4 November 1977, Albuquerque, New Mexico. Abstract in the SIGNi~4 Newsletter, Vol. 12, No. 4 (December 1977), p. 6.

3.12 DONGARHA, J J (1976): Fortran BLAS Timing, LINPACK Working Note No. 3, Applied Mathematics Division, Argonne National Laboratory, Argonne, Illinois 60439.

3.13 DONGARRA, J J (1978): Some LINPACK Timings on the CRAY-I, LINPACK Working Note No. 11, Informal Report LA-7389-MS, Los Alamos Scientific Laboratory, Los Alamos, New Mexico 87545.

3.1h DUFF, I S; REID, J K (1976): A comparison of some methods for the solution of sparse overdetermined systems of linear equations, Journal of the Institute of Mathematics and Its Applications, Vol. 17, pp. 267-280.

3-15 DUFF, I S; ERISMAN, A M; REID, J K (1976): On George's Nested Dissection'Method, SIAM Journal on Numerical Analysis, Vol. 13, pp. 686-695.

3.~6 DUFF, I S (1978): Practical Comparisons of Codes for the Solution of Sparse Linear Systems, Presented at the Symposium on Sparse Matrix Computations, 2-3 November, Knoxville, Tennessee. The proceedings of the symposium will be published by SIAM.

3.]7 DUFF, lain S; REID, John K (1979): Performance evaluation of codes for sparse matrix problems, in "Performance Evaluation of Numerical Software", Proceedings of the IFIP TC 2 Working Conference held in Baden, Austria , 11-15 December 1978, edited by Lloyd D. Fosdick, to be published by North-Holland, Amsterdam.

3.18 EISENSTAT, S C; SCHULTZ, M H; SHERMAN, A H (1975): Application of Sparse Matrix Methods to Partial Differential Equations, In "Advances in Computer Methods for Partial Differential Equations", Proceedings of the AICA International Symposium on Computer Methods for Partial Differential Equations held at Lehigh University - Bethlehem, Pennsylvania, U.S.A. 17-19 June 1975. Edited by H. Vichnevetsky, Available from AICA, Rutgers University, Department of Computer Science, New Brunswick, New Jersey 08903, pp. 40-45.

3.~9 EISENSTAT, S C; SCHgLTZ, M B; SHERMAN, A H (1977): An Auxiliary Storage Method for Solving Large Sparse Positive Definite Systems of Linear Equations, Presented at the SIGNUM Meeting on Mathematical Software, 3-4 November 1977, Albuquerque, New Mexico. Abstract in the SIGNUM Newsletter, Vol. 12, No. 4 (December 1977), p. 4.

3.20 EISENSTAT, S C; SCHULTZ, M H; SHERMAN, A H (1977): Minimal Storage Band Elimination, In "High Speed Computer and Algorithm Organization", edited by David J. Kuck, Duncan H. Lawrie, and Ahmed H. Sameh, Academic Press,'New York 1977, pp. 273-286.

3.21 ELFVING, Tommy (1978): On Computing Generalized Solutions of Sparse Linear Systems with Application to some Reconstruction Problems, LinkOpin4~ Studies in Science and Technology, Dissertations, No. 27, Department of Mathematics, LinkOpin g University, S-58183 Linktping, Sweden.

3.22 EVANS, D J (1973): The Analysis and Application of Sparse Matrix Algorithms in the Finite Element Method, In "The Mathematics of Finite Elements and Applications", Proceedings of the Brunel University conference in April 1972, edited by J. R. Whiteman, Academic Press, London and New York, pp. 427-447.

3.23 FITZGERALD, Kenneth E (1974): Comparison of Some FORTRAN Programs for Matrix Inversion, Journal of Research of the National Bureau of Standards- B. Mathematical Sciences, Vol. 783, No. I, pp. 15-33.

Journal of Computational and Applied Mathematics, volume 5, n o 2, 1 9 7 9 . 149

3.2h GARBOW, B S; BOYLE, J M; DONGARRA, J J; MOLER, C B (1977): Matrix Eigensystem Routines - EISPACK Guide Extension, Lecture Notes in Computer Science, Vol. 51, Springem-Verlag, Berlin-Heidelberg-New York, 343

PP.

3.25 GEORGE, Alan (1977): Numerical Experiments Using Dissection Methods to Solve n by n Grid Problems, SIAM Journal on Numerical Analysis, Vol. 14, pp. 161-179.

3.26 GEORGE, Alan; LIU, Joseph W H (1978): Algorithms for Matrix Partitioning and the Numerical Solution of Finite Element Systems, SIAM Journai on Numerical Analysis, Vol. 15, pp. 297-327.

3.27 GEORGE, Alan; LIU, Joseph W H (1978): An Automatic Nested Dissection Algorithm for Irregular Finite Element Problems, SIAM Journal on Numerical Analysis, Vol. 15, pp. 1053-1069.

3.28 GEORGE, Alan; POOLE, William G; VOIGT, Robert G (1978): Incomplete Nested Dissection for Solving n by n Grid Problems, SIAM Journal on Namerical Analysis, Vol. 15, pp. 662-673.

3.29 GIBBS, Norman E; POOLE, William G; STOCKMEYER, Paul K (1976): A compsmison of several bandwidth and profile reduction alEorithms, &CM Transactions on Mathematical Software, Vol. 2, pp. 322-330.

3.30 GOODMAN, J T; MOLER, C B (1977): Three Numerical Experiments with Gaussian Elimination, LINPACE Working Note No. 8, Technical Memorandum No. 311, Applied Mathematics Division, Argonne National Laboratory, Argonne, Illinois 60439.

3.31 GUSTAFSSON, Ivar (1978): A Class of First Order Pactorization Methods, BIT, Vol. 18, pp. 142-156.

3.32 GUSTAVSON, ~ed G (1978): Two Fast Algorithms for Sparse Matrices: Multiplication and Permuted Transposition, ACM Transactions on Mathematical Software, Vol. 4, pp. 250-269.

3.33 HANSON, Richard J (1969): Certifying Linear Algebra Solvers, SIGNgM Newsletter, Vol. 4, No. 3, October 1969, pp. 21-27.

3.3~ HELLER, D E; STEVENSON, D E; TRAUB, J F (1976): Accelerate iterative methods for the solution of tridiagonal systems on parallel computers, Journal of the Association for Computing Machinery, Vol. 23, pp. 636-654.

3.35 HELLER, Dun (1978): A Survey of Parallel Algorithms in Numerical Linear Algebra, SIAM Review, Vol. 20, pp. 740-777.

3.36 JOHNSON, A I; BARNEY, J R (1976): Numerical solution of large systems of stiff ordinary differential equations in a modular simulation framework, ~n "Numerical Methods for Differential Systems", ed. by L Lapidus and W E Sohiesser, Academic Press, pp. 97-124.

3.37 JORDAN, T L; FONG, Kirby (1977): Some Linear Algebraic Algorithms and Their Performance on CRAY-I, In "High Speed Computer and Algorlthm Organization", edited by David J. Kuek, Duncan H. Lawrie, and Ahmed E. Sameh, Aaademio Press, New York 1977, pp. 313-316.

3.38 JORDAN, Thomas L (1979): A Performance evaluation of linear algebra software in parallel architecture, in "Performance Evaluation of Numerical Software", Proceedings of the IFIP TC 2 Working Conference held in Baden, Austria, 11-15 December 1978, edited by Lloyd D. Fosdick, to be published by North-Holland, Amsterdam.

3.39 KERSBAW, David S (1978): The Incomplete Cholesky-ConJugate Gradient Method for the Iterative Solution of Systems of Linear Equations, Journal of Computational Physics, ¥oi. 26, pp. 43-65.

3.~0 KAGSTR~M, Be (1977): Bounds and Perturbation Bounds for The Matrix Exponential, BIT, Col. 17, pp. 39-57.

3.~I KAGSTROM, Be (1977): Numerical Computation of Matrix Functions, Report UMINF-58.~7, Department of Information Processing, University of UNeA, S-90187 gme~, Sweden.

3.42 LAMBIOTTE Jr, Jules J; VOIGT, Robert G (1975): The Solution of Tridiagonal Linear Systems on the CDC STAR-100 Computer, ACM Transactions on Mathematical Software, Vol. I, pp. 308-329.

3.h3 LAWSON, C L (1974): Standardization of Fortran Callable Subprograms for Basic Linear Algebra, In "Mathematical Software II", Informal Proceedings of a Conference, edited by John R Rice. Purdue Universfty, May 29-31, 1974, p. 261.

3.4~ LAWSON, C L; EKELUND, J (1977): An Out-of-Core Leas t Squares Program, Presented at the SIGNUM Meeting on Mathematical Software, 3-4 November 1977, Albuquerque, New Mexico. Abstract in the SIGNUM Newsl~tter, Vol. 12, No. 4 (December 1977), p. 5.

3.45" MADSEN, Niel K; RODRIGUE, Garry R (1976): A comparison of direct methods for tridiagonal systems on the CDC STAR-100, Preprint UCRL-76993, Roy. I, May 1976, Lawrence Liver~ore Laboratory.

3.~6 McCLELLAN, M T (1973): The Exact Solution of Systems of Linear Equations with Polynomial Coefficients, Journal of the Association for Computing Machinery, Vol. 20, pp. 563-588.

3.h7 McCLELLAN, Michael T (1977): The Exact Solution of Linear Equations With Rational Function Coefficients, ACM Transactions on Mathematical Software, Vol. 3, pp. 1-25.

3.h8 McCLELLAN, Michael T (1977): A Comparison of Algorithms for the Exact Solution of Linear Equations, ACM Transactions on Mathematical Software, Col. 3, PP. 147-158.

3.49 MEIJERINK, J A; van de r VORST, H A (1977): An I t e r a t i v e So lu t ion Method for L inear Systems o f Which the Coefficient Matrix is a Symmetric M-Matrix, Mathematics of Computation, Vol. 31, pp. 148-162.

3.50 MOLCHANOV, Igor (1979): Performance evaluation of linear algebra software, in "Performance Evaluation of Numerical Software", Proceedings of the IFIP TC 2 Working Conference held in Baden, Austria, 11-15 December 1978, edited by Lloyd D. Fosdick, to be published by North-Holland, Amsterdam.

3.51 MOLER, Cleve B (1974): Software for Matrix Computations, In "Mathematical Software II", Informal Proceedings of a Conference, edited by John R Rice. Purdue University, May 29-31, 1974, pp. 307-321.

3.52 MOLER, Cleve; van LOAN, Charles (1976): Nineteen Dubious Ways to Compute the Exponential of a Matrix, SIAM Review, Vol. 20, pp. 801-836.

3.53 NEWBERY, A C R (1975): Quality tests for linear equation solvers, Department of Computer Science, University of Kentucky, Technical Report No. 18-75. 20 pp.

3.5h NORIN, Robert S (1978): Sparse Matrix Calculations Using an Array Processor, Proceedings of COMPSAC78, The IEEE Computer Society'~ Second International Computer Software & Applications Conference, IEEE Catalog No. 78CHI338U3C, pp. 183-187.

3.55 PANTTAJA, J~es (1974): A Comparison of the PLU and QR Methods for Determining Eigenvalues of Real Hessenberg Matrices, In "Mathematical Software II", Infor~lal Proceedings of a Conference, edited by John R Rice. Purdue University, May 29-31, 1974, p. 252.

3.56 PARLETT, E N; WANG, X (1975): The Influence of the Compiler on the Cost of Mathematical Software - in Particular on the Cost of Triangular Factorization, ACM Transactions on Mathematical Software, Vol. I, pp. 35-46.

3.57 PEREYRA , V; SCHERER, Godela (1973): E igenva lues o f S~11etric Tridlagonal Matrices: A Fast, Accurate and Reliable Algorithm, Journal of the Institute of Mathematics and Its Applications, Vol. 12, pp. 209-222.

3.58 de PILLIS, John (1978) Faster Convergence for Iterative Solutions to Systems via Three-Part Splittings, SIAM Journal on Numerical Analysis, Vol. 15, pp. 888-911.


3.59 REDISH, K A; WARD, W A (1971): S,-,m~.y of "Eigenvalue and Elgenvector Routines in the MoMaster Program Library", SIGNL~ Newsletter, Vol. 6, No. 2, May 1971, pp. 8-9.

3.60 REID, d E (1977): Sparse Matrices, In "The State of the Art in Numerical Analysis", edited by D. A. B. Jaeobs, Academic Press, London, pp. 85-146.

3.61 RUHE, Axel; KAGSTR~M, Be (1977): Numerical Computation of Matrix Functions, Presented at the SIAM 1977 Fall Meeting, 31 October - 2 November, Albuquerque, New Mexico. Abstract in SIAM Review, Vol. 20 (1978), p. 634.

3.62 SANDERSON, Jim (1976): A Proof of Convergence for the Tridiagonal QL Algorithm in Floating-Point Arithmetic, Presented at the SIAM 1976 Fall Meeting, Atlanta, Georgia, 18-20 October 1976. Abstract in SIAM Review, Vol. 19 (1977), p. 778.

3.63 SHERMAN, Andrew H (1978): On Newton-Iterative Methods for the Solution Gf Systems of Nonlinea~ Equations, SIAM Journal on Numerical Analysis, Vol. 15, pp. 755-771.

3.64 S~ERMAN, Andrew H (1978): Algorithms for Sparse Gaussian Elimination with Partial Pivoting, ACM Transactions on Mathematical Software, Vol. 4, pp. 330-338.

3.65 S~ITH, B T; BOYLE, J M; DONGARRA, J J; GARBOW, ~ S; IKEBE, Y; ELK~A, V C; MELEE, C B (1976): Matrix Eigensystem Routines - EISPACK Guide, Second Edition, Lecture Notes in Computer Science, Vol. 6, Springer-Verlag, Berlin-Heldelberg-New York, 551 pp.

3.66 SMITH, Brian T (1979): Can automated theorem provers be used to evaluate linear algebra software? in "Performance Evaluation of Numerical Software", Proceedings of the IFIP TC 2 Working Conference held in Baden, Austria, 11-15 December 1978, edited by Lloyd D. Fosdick, to be published by North-Holland, Amsterdam.

3.67 SMITH, D A; GUIPRE, Pamela S (1978): Modifications to the Forsythe-Moler algorithm for solving linear algebraic systems, The Computer Journal, Vol. 21, pp. 174-177.

3.68 SPARKS, D N; TODD, A D (1973): A Comparison of Fortran Subroutines for Calculating Latent Roots and Vectors, Journal of the Royal Statistical Society, Series C (Applied Statistics), Vol. 22, pp. 220-225.

3.69 SPIESS, J (1976): Investigations" of speed-ups by new algorithms for matrix multiplication, Computing, Vol. 17, pp. 23-36.

3.70 TUTTLE, P G; BROWN, R L (1975): The Implemen ta t ion o f Selected Eigenvalue Algorithms on a Vector Computer, Presented at the SIAM-SIGNUM 1975 Fall Meeting, 3-5 December, San Francisco, California. Abstract in SIAM Review, Vol. 18 (1976), p. 831.

3.7] WANG, H H (1976): On Some Experience using the SSOR and Related Methods for the Numerical Solution of Diffusion Equation, Presented at the SIAM 1976

• National Meeting, 16-18 Jt~e, Chicago, Illinois. Abstract in SIAM Review, Vol. 19 (1977), p. 400.

3.72 YOUNG, David M (1976): Iteratlve Solution of Linear Systems Arising from Finite Element Techniques, In "The Mathematics of Finite Elements and Applications II, MAFELAP 1975", Proceedings of the Brunel University conference in April 1975, edited by J. R. Whiteman, Academic Press, London and New York, pp. 439-464.

3.73 ZIELKE, Gerhard (1978): Test Matrlees for Generalized Inverses, SIGNt~ Newsletter, Vol. 13, No. 4, December 1978, pp. 10-12.

4. OPTIMIZATION AND NONLINEAR EQUATIONS

4.01 BJ~RCK, Ake (1975): Methods for Sparse Linear Least Squares Problems, Report LiTH-MAT-R-75-10, Department of Mathematics, Linktping University, S-58183 Linktping, Sweden.

4.02 EJORCK, Ake (1976): Ccament'on the Iterative Refinement of Least Squares Solutions, Report LiTH-MAT-R-76-q, Department of Mathematics, Linktplng University, 8-58183 Linktping, Sweden.

~.03 BLUE, James L (1978): Robust Algorithms for Solving Systems of Nonlinear Equations, Computing Science Technical Report No. 67, Bell Laboratories, Murray Hill, New Jersey 07974.

~Oh BOLAND, W R; KOWALIK, J S (1977): Extended Conjugate Gradient Methods, Prdsented at the SIGNUM Meeting on Mathematical Software, 3-4 November 1977, Albuquerque, New Mexico. Abstract in the SIGNUM Newsletter, Vol. 12, No. 4 (December 1977), p. 7.

h.05 BRENT, E P (1975): Multiple-precision zero-finding methods and the complexity of elementary function evaluation, in "Analytic Computational Complexity", edited by J. F. Traub, Academic Press, New York, pp. 151-~76.

h.06 BHENT, R P (1978): A Fortran multiple-precision arithmetic package, ACM Transactions on Mathematical Software, Col. 4, pp. 57-81.

4.07 COLVILLE, A R (1970): A Comparative Study of Nonlinear Programming Codes, in "Proceedings of the Princeton Symposium on Mathamatinal Programming", edited by H. W. Kuhn, Princeton University Press, Princeton, New Jersey.

~.08 COSNARD, M; MORE, J J (1975): Numerical Comparison of Nonlinear Equation Solvers, Presented at the SIAM-SIGNUM 19.75 Fall Meeting, 3-5 December, San Francisco, California. Abstract in SIAM Review, Vol. 18 (1976), p. 818.

h~09 DENNIS, J (1977): Non-linear Least Squares and Equations, In "The State of the Art in Numerical Analysis", edited by D. A. H. Jaeobs, Academic Press, London, pp. 269-312.

A.IO DENNIS, J E; SCHNABEL, R B (1978): Least Change Secant Updates f o r Quasi-Newton Methods, Presented at the SIAM 1978 Fall Meeting, October 30 - November I, Knoxville, Tennessee.

5.11 EASON, E D; FENTON, R G (1974): A Comparison of Numerical Optimization Methods for Engineering Design, Journal of Engineering fo~ Industry, Trans. A.S.M.E., Vol. 96, Series B, No. I, pp. 196-200.

4.12 ELDEN, Larm (1977): Algorithms for the Regularization of Ill-Conditioned Least Squares Problems, BIT, Vol. 17, pP. 134-145.

~.13 ELFVING, Tommy (1975): Some Numerical Results Obtained with two Gradient Methods for Solving the Linea~ Least Square Problems, Report LiH-MA~-R-75-5, Department of Mathematics, Linktping University, S-58183 Linktping, Sweden.

4.1h GILL, Philip E; MURRAY, Walter (1978): Algorithms for the Solution of the Nonlinear Least-Squares Problem, SIAM Journal on Numerical Analysis, Vol. 15, pp. 977-992.

4.15 GREENBERG, Harvey J (1978): Design and Implementation of Optimization Software, Proceedings of the NATO Advanced Study Institute on Design and Implementation of Optimization Software, Urbino, Italy, 20tb June-2nd July 1977~ NATO Advanced Study Institute Series E: Applied Science - No. 28, Si~thoff & Noordhoff International Publishers, Alphen aan den Rijn, The Netherlands, 566 pp.

~.16 HASKELL, K H;HANSON, R J (1977): An Algorithm and Fortran Code for the Linearly Constrained Least Squares Problem, Presented at the SIGNL~4 Meeting on Mathematical Software, 3-4 November 1977, Albuquerque, New Mexico. Abstract in the SIGNSM Newsletter, Vol. 12, No. 4 (December 1977), p. 13.

4.17 HILLSTHCt4, Kenneth E (1977): A Simulation Test Approach to the Evaluation of Nonlinear Optimization Algorithms~ ACM Transactions on Mathematical Software, Vol. 3, PP. 305-315.

4.18 IDA, Tetsuo; GOTO, Eiiohi (1978): Overflow Free and Variable Precision Computing in FLATS, J. Information Processing, Vol. 1, pp. 140-142.

~.19 LARICHEV, O I; GORVITS, G G (1974): New Approach to Comparison of Search Methods Used in Nonlinear Programming Problems, Journal of Optimization Theory and Applications, Vol. 13, PP. 635-659.

Journal of Computationad and Applied Mathematics, volume 5, no 2, 1979. 151

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4.22

4.23

.24

4.25

4.26

4.27

4.28

4.29

4.30

4.31

4.32

2.33

4.34

4.35

LASDON, L S; WAREN, A D; JAIN, A; RATNER, M (1978): Design and Testing of a Generalized Reduced Gradient Code forNonlinear Programming, ACM Transactions on Mathematical Software, Vol. 4, pp. 34-50.

LAWSON, Charles L; HANSON, Richard J (1974): Solving Least Squares Problems, Prentice-Hall, Englewood Cliffs, New Jersey, 340 pp.

LZNESS, j N (1977): On the Nature of Benchmark Problems for Evaluating Optimization Routines, Presented at the SIGNUM Meeting on Mathematical Software, 3-4 November 1977, Albuquerque, New Mexico. Abstract in the SIGNUM Newsletter, Vol. 12, No. 4 (December 1977), p. 8.

MAHENDHARAJAH, A; FIALA, F (1976): A comparison of three algorithms for linear zero-one programs, ACM Transactions on Mathematical Software, Vol. 2, pp. 331-334.

MORE, J (1977;: Software for Nonlinear Optimization Problems, Presented at the SIGN[~4 Meeting on Mathematical Software, 3-4 November 1977, Albuquerque, New Mexico. Abstract in the SIGNUM Newsletter, Vol. 12, No. 4 (December 1977), p. 6.

MORE, Jorge J (1979): Developing and testing quality optimization software, in "Performance Evaluation of Numerical Software", Proceedings of the IFIF TC 2 Working Conference held in Baden, Austria, 11-15 December 1978, edited by Lloyd D. Fosdick, to be published by North-Holland, Amsterdam.

MURRAY, Walter; GILL, Philip E (1979): Performance evaluation for optimization software, in "Performance Evaluation of Numerical Software", Proceedings of the IFIP TC 2 Working Conference held in Baden, Austria, 11-15 December 1978, edited by Lloyd D. Fosdick, to be published by North-Holland, Amsterdam.

NERINCKX, D;HAEG~ANS, A (1976): A Comparison of Non-Linear Equation Solvers, Journal of Computational and Applied Mathematics, Vol. 2, pp. 145-148.

PAIGE, C C; SAUNDERS, M A (1977): Least Squares Estimation of Discrete Linear Dynamic Systems Using Orthogonal Transformations, SIAM Journal on Numerical Analysis, Vol. 14, pp. 180-193.

POWELL, M J D (1975): A View of Unconstrained Minimization Algorithms That Do Not Require Derivatives, ACM Transactions on Mathematical Software, Vol. I, pp. 97-107.

RAMSIN, H~kan (1973): Metoder och program f t r iekalinJ~ optimering, (Methods and Programs for Non-linear Optimization, in Swedish). ITMWorking Paper No. 4. Swedish Institute of Applied Mathematics, Stockholm, Sweden.

RAMSIN, R~kan; WEDIN, Per-Ake (1977): A eompsrison of some algorithms for the nonlinear least squares problem, BIT, Vol. 17, pp. 72-90.

SCHITTKOWSKI, K; ZIZ~4ERMAN, P (1977): A factorization method for constrained least squares prpblems with data changes. Part 2: Namerieal tests, comparisons, and ALGOL-codes. Preprlnt No. 30, Institut fuer Angewandte Mathematik und Statistik, Bniversitlt Wuemzburg.

SCHITTKOWSKI, Klaus (1979): Numerical comparison of optimization software USing randomly generated test problems, in "Performance Evaluation of Numerical Software", Proceedings of the IFIP TC 2 Working Conference held in Baden, Austria, 11-15 December 1978, edited by Lloyd D. Fosdick, to be published by North-Holland, Amsterdam.

SCHITTKOWSKI, K; STOER, J (1979): A Factorization Method for the Solution of Canstralned Linear Least Squares Problems Allowing Subsequent Data Changes, Numerisehe Mathematik, Vol. 31, pp. 431-463.

SC~R4IDT, Joehen W; HOYER, WolfEang (1978): Die Verfahren vum Brown-Brent-Typ bei gemischt linearen-niehtlinearen Oleichungssystemen, ZAMM, Vol. 58, pp. 425-q2~.

2.36 SCHNABEL, Robert B (1979): Two aspects affecting development, testing, and performance of software for unconstrained optimization, in "Performance Evaluation of Numerical Software", Proceedings of the IFIP TC 2 Working Conference held in Baden, Austria, 11-15 December 1978, edited by Lloyd D. Fosdick, to be published by North-Holland, Amsterdam.

4.37 SCHULTZ, Reinhart (19782: Ein Abstiegsvsfahren fuer Approximationsaufgaben in normierten R~umen (A Descent Method for Approximation Problems in Normed Spaces, in German), Numerische Mathematik, Vol. 31, pp. 77-95.

2.38 SPEDICATO, E; GREENSTADT, J (1978): On Some Classes of Variationally Derived Quasi-Newton Methods for Systems of Nonlinear Algebraic Equations, Numerische Mathematik, Vol. 29, pp. 363-380.

4.39 SWIFT, A; LINDFIELD, G R (1978): Comparison of s continuation method with Brent's method for the numerieal solution of a single nonlinear equation, The Computer Journal, Vol. 21, pp. 359-362.

.4.40 ~IDINT, Ph L (1978): Some Numerical Results Using a Sparse Matrix Updating Formula in Unconstrained Optimization, Mathematics of Computation, Vol. 32, pp. 839-851.

4.41 WAMPLER, R H (1970): On the accuracy of least squares computer programs, Journal Amer. Star. Assoc., Vol. 65, pp. 549-565.

4.~2 WAREN, A D; LASDON, L S (1977): A survey of nonlinear programming software, in "Proceedings of the ACM 1977 Annual Conference", ACM, New York, pp. 275-282.

4.43 WAREN, A D; LASDON, L S (1978): The Status of Nonlinear Programming Software, Manuscript, Department of Computer and Information Seienoe, Cleveland State University, Cleveland, Ohio 44115.

2.44 WATERMAN, R J (1976): An Evaluation and Comparison of Three Nonlinear Programming Codes, M.S. Thesis, Naval Postgraduate School, Monterey, California.

4.45 WEISS, Rotraut (1973): A Comparative Study of Multidimensional Function Optimlzers, CGTM No. 148, SLAC Computation Group, Stanford, California.

5. FUNCTIONS

5.01 AMOS, D E; DANIEL, S L; WESTON, M K (1977): CDC 6600 Subroutines IBESS and JBESS for Bessel Functions I(n,x) and J(n,x), x >= 0, n >= O, ACM Transactions on Mathematical Software, Vol. 3, PP. 76-92.

5.02 BRENT, R P (1976): Fast Multiple-Precision Evaluation of Elementary Functions, Journal of the Association for Computing Machinery, Vol. 23, pp. 242-251.

5.03 CLARK, N A; CODY, W J; HILLSTROM, K E; THIELIEKER, g A (1967): Performance Statistics for the FORTRAN IV (H) LIBRARY for the IBM SYSTEM/360, SICNUM Newsletter, Vol. 2, No.3, December 1967, 7 pp.

5.04 CLENSHAW, C W (1974): Rational approximations for special fuhctions, In "Software for Numerical Mathematics", edited by D. J. Evans, Academic Press, London, pp. 275-284.

5.05 CODY, W J (1969): Performance Testing of Function Subroutimes, AFIPS Conference Proceedings, Spring Joint Computer Conference, pp. 759-753.

5.06 CODY, W J (1971): Software for the elementary ftmotions, In "Mathematical Software", edited by John R. Rice, Aeademim Press, New York, pp. 171-186.

5.07 CC~Y, W J (1975): The FUNPACK Package of Special Function Subroutines, ACM Transactions on Mathematical Software, Vol. I, pp. 13-25.

5.08 CODY, W J (1976): An overview of software development for special functions, Lecture Nohes in Mathematics, Vol. 506, Springer Verlag, Berlin 1976, PP. 38-48.

5.09 CODY, W J (1977): Transportable Test Programs for Elementary Functions, Presented at the SIGND]~ Meeting on Mathematical Software, 3-4 November 1977, Albuquerque, New Mexico. Abstract in the SIGNDM Newsletter, Vol. 12, No. 4 (December 1977), p. 15.


5.10 CODY, W J; MOTLEY, Rose M; FULLERTON, L Wayne (1977): The Computation of Real Fractional Order Bessel Functions of the Second Kind, ACM Transactions on Mathematical Software, Vol. 3, PP. 232-239.

5.11 COPY, W J (1977): The challenge in numerical software for microcomputers, Proceedings Ist Annual Rocky Mountain Symposium on Microcomputers, IEEE Computer Society, PP. 1-23.

5.12 COX, W M (1971): UNIVAC Claims Super Accurate Fortran Math Library, SIGNL~4 Newsletter, Vol. 6, No. 3, November 1971, p. 9.

5.13 FIKE, C T (1968) Computer Evaluation of Mathematical Functions, Prentice Mall, New Jersey.

5.14 FULLERTON, L Wayne (1977): Portable Special Function Routines, In "Portability of Numerical Software", edited by Wayne Cowell, Lecture Notes in Computer Science, Vol. 57, Springem-Verlag, Berlin, pp. 452-483.

5.15 FULLERTON, L W (1977): A Portable Library of Mathematical Functions, Presented at the SIGNUM Meeting on Mathematical Software, 3-4 November 1977, Albuquerque, New Mexico. Abstract in the SIGNUM Newsletter, Vol. 12, No. 4 (December 1977), P. 12.

5.16 GAUTSCHI, Walter (1977): Evaluation of the Repeated Integrals of the Cosrror Function, ACM Transactions on Mathematical Software, I/ol. 3, PP. 240-252.

5.17 GAUTSCNi, Walter; SLAVIE, Josef (197~): On the Computation of Modified Bessel Function Ratios, Mathematics of Computation, Vol. 32, pp. 865-875.

5.18 GUSTAF~ON, S-$ (1978): Convergence Acceleration on a General Class of Power Series, Computing, Vol. 21, pp. 53-69~

5.19 HART, d Fet al (1968): Computer Approximations, Wiley, NeW York, 343 pp.

5.20 HILLSTROM, K E (1970): Performance statistics for the FORTRAN IV (H) and PL/I (Version 5) Libraries in IBM OS 360 Release 18, Report AWL-7666, August 1970, Argonne National Laboratory.

5.21 NO, J C; SCHRYER, N L (1976): Implementation of Supplementary Elementary Functions for the Port Library, Computing Science Tee/~nieal Report No. 43, Hell Laboratories.

5.22 KAHAN, W (1972): Hirondo Kuki in memoriam, SIGNDM Newsletter, Vol. 7, No. I, April 1972, pp. 8-10.

5.23 K~4P, P (1977): Writing the Elementary Function Procedures for the ALGOL68C Compiler, In "Portability of Numerleal Software", edited by Wayne Cowell, Lecture Notes in Computer S~ienoe~ Vol. 57, Springer-Verlag, Berlin, pp. 127-144.

5.2~ K~KI, H (1971): Mathematical Function Subprograms for Basic System Libraries - Objectives, Constraints and Trade-Off, In "Mathematical Software", edited by John R. Rice, Academic Press, New York, pp. 187-199.

5.25 KUKI, H; ASCOLI, J (1971~: FORTRAN extended-precision library, IBM Systems Journal, Vol. I0, pp. 39-61,

5.26 LOZIER, D Wet al (1971): A Bit Comparison Program for Algorithm Testing, National Bureau of Standards, Washington D.C., Report 10-449.

5.27 LNKE, Yudell L (1975): Mathematical Functions and Their Approximation. Academic Press, New York.

5.28 NEWBERY, A C R; LEIGH, Ann P (1971): Consistency Test for Elementary Functions, AFIre Proceedings, Vol. 39, Fall Joint Computer Conference, pp. 419-422.

5.29 NG, Edward W (1975): A Comparison o f Computational Methods and Algorithms for the Complex Gamma Function, ACM Transactions on Mathematical Software, Vol. 1, pp. 56-70 .

5.30 NG, E W (1977): A Comparison of Computational Algorithms and Software for the Complex Error Function and Related Functions, Presented at the SIGNI~M Meeting on Mathematical Software, 3-4 Novem~ber 1977, Albuquerque , New Mexico. Abstract in the SIGNUM Newsletter, Vol. 12, NO. 4 (December 1977), p. 15.

5.31 PAUL', George; WILSON, M Wayne (1976): Should the Elementary Function Library Be Incorporated Into Computer Instruction Sets? ACM Transactions on Mathematical Software, Vol. 2, pp. 132-142.

5.32 SCHONFELDER, j L (1979): Special Functions in the NAG Library, In "Software for Numerical Mathematics", edited hyD. J. Evans, Academic Press, London, pp. 285-300 .

5 .33 SCHONFELDER, J L (1976) : The P r o d u c t i o n o f S p e c i a l Function Routines for A Multi-Machine Library, Software-Practice and F2xperience, Vol. 6, pp. 71-82.

5.3~ SCHONFELDER, J L (1977): The Production and Testing of Spaolal Function Software in the NAG Library, In • Portability of Nomerinal Software", edited by Wayne Cowell, Lecture Notes in Computer Sciences Vol. 57, Springer-Verlag, Berlin, pp. 425-451.

5.35 TURNER, L Richard (1969): Difficulty in Sin/Cos Routine, SIGNUM Newsletter, Vol. 4, No. 3, October 1969, p. 13.

5.36 WALLACW, W (1969): FORTRAN V Library Functions Reference Manual for UNIVAC 1108, University of Wisconsin, Madison, Wisconsin.

5.37 WALTHER, J S (1971): A unified algorithm for elementary functions, AFIPS Proceedings, Vol. 38, Spring Joint Computer Conference, pp. 379-385.

5.38 WANG, J Y (1978): The Evaluation of Periodic Functions with Large Input Arguments, SIGNOM Newsletter, Vol. 13, No. ~, December 1978, pp. 7-9.

5.39 WYATT, W T; LOZIER, D W; ORSER, D J (197b): A portable extended precision arithmetic package and library with Fortran precompiler, ACM Transactions on Mathematical Software, Vol. 2, pp. 209-231.

6. QUADRATURE

6.01 BLAKEMOEE, M; EVANS, G A; NYSLOF, J (1976): Comparison of some methods for evaluating infinite range oscillatory integrals, Journal of Computational Physics~ Vol. 22, pp. 352-376.

6.02 BLUE, James L (1977): Automatic Numerical Quadrature, The Bell System Technical Journal, Vol. 56, No. 9, pp. 1651-1678.

6.03 CASALETTO, J; PICKETT, M; RICE, J (1969): A comparison of some numerical integration programs, SIGNDMNewsletter, Vol. 4, No. 3, PP. 30-40."

6.0~ DAVIS, Philip J; RABINOWITZ, Philip (1975): MethOds of Numerical Y.ntegration, Academic Press, New York, 459 pp.

6.05 de BOOR, Carl (1971): On Writing an Automatic Integration Algorithm, In ,Mathematical Software", edited by John R. Rice, Academic Press, New York, pp. 201-209.

6.06 de BOOR, Carl (1971): CADRE: An Algur l thm fo r Numerical QuadratUre, In .Mathematical Software", edited by John R. Rice, Academic Press, New York, pp. ~17-449.

6.07 de DONCKER, E; PIgWeEdS, R (1976): Measurement of Quality of Quadrature Routines, Manuscript, Applied Mathematics and Programming Division, University of Leuven, January 15, 1976, 11 pp.

6.08 de DONCKER, E; FIESSENS, R (1976): A BibliographY on Automatic Integration, Journal of Computational and Applied Mathematics, Vol. 2, pp. 273-280.

6.09 de DONCKER, Elise; FIESSENS, Robert (1977): Automatic Computation of Integrals with Singular InteErand, Over a Finite or an Infinite Range, Computing, Vol. 17, pp. 265-279.

6.10 de DONCKER, Elise (1978): An Adaptive Extrapolatlon Algorithm for Automatic Integration, S~GNUM Newsletter, Vol. 13, No. 2 (June 1978), PP. 12-18.

6.11 DIXON, Valerie A (1974): Numerical quadrature: a survey of the available algorithms, In ,Software for Numerical Mathematics", edited by D. d. Evans, Academic Press, London, pp. 105-137.

Journal of Computational and App~ed Mathematics, volume 5, no 2, 1979. 153

6.12 EINARSSON, Bo (1972): On the Calculation of ~ourier Integrals, In "Information Processing 71", Proceedings of IFIP Congress 71 in LJublJana, August 23-28, 1971. Ed. by C. V. Freiman, North-Holland Publishing Company, Amsterdam, pp. 1346-1350.

6.13 EINARSSON, Bo (1974): Testing and Evaluation of Some Subroutines for Numerical Quadrature, In "Software for Numerical Mathematics", edited by D. J. Evans, Academic Press, London, pp. 149-157.

6.14 EINARSSON, Bo (1976;: Use of Richardson Extrapolation for the Numerical Calculation of Fourier Transforms, Journal of Computational Physics, Vol. 21, pp. 365-370.

6.15 FAIRWEATHER, G; KEAST, P (1976): A Comparison of Non-Adaptive Romberg Quadrature Routines, Technical Report No. 96, Department of Computer Science, University of Toronto.

6.16 FAIRWEATHER, Graeme; KEAST, Pat (1978): An Investigation of Romberg Quadrature, ACM Transactions on Mathematical Software, Vol. 4, pp. 316-322.

6.17 FRITSCH, F N (1973): Cc~parative Study of Automatic Two-Dimensional Integration Routines, I. Measures of Comparison, UCRL-75200, November 1973, 17 pp., Lawrence Livermore Laboratory.

6.18 GALLAHER, L J (1976): Adaptive quadrature and proof of program correctness, Presented at the SIAM 1976 Fall Meeting, Atlanta, Georgia, 18-20 October 1976.

6.19 GARRIBBA, S; QUARTAPELLE, L; REINA, G (1978): Algorithm 36 - SNIFF:Efficlent Self-Tuning Algorithm for Numerical Integration, Computing, Vol. 20, pp. 363-375.

6.20 HAUSNER, Arthur (1977): NL9 - An Adaptive Routine for Numerical Quadrature, In the ProceedIngs of the 1977 Numerical Analysis and Computers Conference, 30-31 March, Madison, Wisconsin. ARC Report 77-3, U S Army Research Office, Research Triangle Park, North Carolina, pp. 367-410.

6.21 HAZLEW0OD, L J (1977): An Alternative Strategy for Cautious Adaptive Quadrature, Journal of the Institute of Mathematics and its Applications, Vol. 20, No. 4, pp. 505-518.

6.22 HOOVER, W E; FRAME, J S (1977): Some Multidimensional Quadrature Formulas Using Partial Derivatives, Presented at the SIAM 1977 Fall Meeting, 31 October - 2 November, Albuquerque, New Mexico. Abstract in SIAM Review, Vol. 20 (1978), p. 627.

6.23 JACOBS, F J (1975): Truncation Error and Modified Romberg Extrapolation for the Filon-Trapezoidal Rule, T.H.-Report 75-WSK-03, Department of Mathematics, Technological University Eindhoven, Netherlands.

6.2~ JONES, R (1973): Results of some quadrature tests, unpublished.

6.25 KAHANER, D E (1971~: Com~rison of numerical quadrature formulas, In "Mathematical Software", edited by John R. Rice, Aomdemio Press, New York, pp. 229-259.

6.26 KAHANER, David (1976): Report on the Los Alamos quadrature workshop, SIGNUM Newsletter, Vol. 11, No. I, May 1976, pp. 4-26.

6.27 EEAST, Patrick (1975): The evaluation of one-dimensional quad=ature routines, Technical Report No. 83, Department of Computer Science, University of Toronto.

6.28 KROGR F T; SNYDER, W V (1975):" Preliminary Results with a New Quadrature Subroutine, Jet Propulsion Laboratory, Section 914, Computational Memorandum No. 363, Revised April 1975, Pasadena, California.

6.29 KROGH, F T; SNYDEE, W V (1977): Comparison of Software for Numerical Quadrature, Presented at the SIAM 1977 Fall Meeting, 310mtober - 2 November, Albuquerque, New Mexico. Abstract in SIAM Review, Vol. 20 (1978), p. 634.

6.30 EROGH, Fred T; SNYDER, W V (1977): Test Results with Quadrature Software 1977, Report CL77-576, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California.

6.31 LYNESS, J N (1968): Some Interesting Quadrature Tests, SICNUM Newsletter, Vol. 3, No. 2, July 1968, Ip.

6.32 LYNESS, J N (1969): GAUSS Versus ROMBERG, SIGNUM Newsletter, Vol. 4, No. I, January 1969, p. 9.

6.33 LYNESS, J N (1972): Guidelines for automatic quadrature routines, In "Information Processing 7.1", Proceedings of IFIP Congress 71 in Ljubljana, August 23-28, 1971. Ed. by C. V. Freiman, North-Holland Publishing Company, Amsterdam, pp. 1351-1355.

6.3h LYNESS, J N (1976): When not to use an automatic quadrature routine, Presented at the SIAM 1976 Fall Meeting, Atlanta, Georgia, 18-20 October 1976. Abstract in SIAM Review, Vol. 19 (1977), p. 773.

6.35 LYNESS, J N; KAGANOVE, J J (1976): Comments on the nature of automatic quadrature routines, ACM Transactions on Mathematical Software, Vol. 2, pp. 65-81.

6.36 LYNESS, d N; KAGANOVE, d d (1977): A technique for comparing automatic quadrature routines, The Computer Journal, Vol. 20, pp. 170-177.

6.37 LYNESS, J N (1977): Quid, Quo, Quadrature? In "The State of the Aft'in Numerical Analysis", edited by D. A. H. Jacobs, Academic PreSs, London, pp. 535-560.

6.38 MALCOLM, Michael A; SIMPSON, R Bruce (1975): Local Versus Global Strategies for Adaptive Quadrature, ACM Transactions on Mathematical Software, Vol. I, pp. 129-146.

6.39 OLIVER, J (1972): A doubly-adaptive Clenshaw-Curtis quadrature method, The Computer Journal, Vol 15, pp. 141-147.

6.hO PATTERSON, T N L (1973): Algorithm 468 : Algorithm for automatic numerical integration over a finite interval, Ccamunioations of tbe ACM, Vol. 16, pp. 694-699.

6.41 PIESSENS, R (1973): An algorithm for automatic integration, Angewandte Informatik, Vol. 15, pp. 399-40 I.

6.~2 PIESSENS, Robert (1975;: An Automatic Routine for the Integration of Oscillatory Functions, Report TW 30, Applied Mathematics and Programming Division, University of Leuven, November 1975.

6.43 PIESSENS, Robert; de DONCKER, Elias (1975): "Testing a New One-Dimensional Quadrature Routine, (preliminary results), Report TW 24, Applied Mathematics and Programming Division, University of Leuven, July 1975.

6.~4 PIESSENS, R; de DONCKER, E (1976): Testing and Comparison of Quadrature Routines, Manuscript, Applied Mathematics and Programming Division, University of Leuven, Jantmry 15, 1976, 22 pp.

5.45 RICE, John R (1976): The algorithm selection problem, In "Advances in Computers", Vol. 15, Edited by M. Rubinoff and M. C. Yoritz, Academic Press, New York 1976, pp. 65-118. - Section 3, The Selection of Quadrature Algorithms, pp. 77-82.

6.~6 3ASAKI, Tateaki (1978): Multidimensional Monte Carlo Integration Based on Factorized Approximation Functions, SIAM Journal on Numerical Analysis, Vol. 15, pP. 938-952.

6.~7 STETTER, Hans J; UEBERHUBER, Christoph W (1975): Proposal for population studies in numerical quadrature, Journal of Computational and Applied Mathematics, Vol. I, pp. 213-215.

6.48 TOMPA, H (1969): Remberg Versus GAUSS, SIGN~ Newsletter, Vol. 4, No. I, January 1969, p. 8.

6.~9 UEBERHUBER, Cbristoph W (1976): A Program-package for Numerical Quadrature, Presented at the SIAM 1976 National Meeting, 16-18 June, Chicago, Illinois. Abstract in SIAM Review, Vol. 19 (1977), P. 399.

7. INTEGRAL EQUATIONS

7.01 ANDERSSEN, R S (1978): Stable procedures for the inversion of Abel°s equation, Journal of the Institute of Mathematics and Its Applications, Vol.

17, PP. 329-342.

Journal of Computational and Applied Mathematics, volume 5, no 2, 1 9 7 9 . 154

7.02 ATKINSON, Kendall E (1976): A Survey of Numerical Methods for the Solution of Fredholm Integral Equations of the Second Kind, SIAM, Philadelphia, 230

PP.

7.03 ATKINSON, Kendall (1976): An Automatic Program for Linear Fredholm Integral Equations of the Soeond Kind, ACM Transactions on Mathematical Software, Vol. 2, pp. 154-171.

7.0~ BAKER, C T H (1977): The Numerical Treatment of Integral Equations, Clarendon Press, Oxford, 1034 pP.

7.05 BAKER, Christopher T H; KEECH, Malcolm S (1978): Sgahility Regions in the Numerical Treatment of Volterra Integral Equations, SIAM Journal on Numerical Analysis, Vol. 15, pp. 394-417,

7.06 BAKER, Christopher T H; KEECE, Malcolm S (1978): Stability Analysis Of Certain Runge-Kutta Procedures for Volterra Integral Equations, ACM Transactions on Mathematical Software, Vol. 4, pp. 305-315.

7.07 BHANCA, H W (1978): The ~onlinear Volterra Equation of Abel's Kind and Its Nemerioal Treatment, Computing, Vol. 20, pp. 307-324.

7.08 DELVES, L M (1974): An Automatic Ritz-Galerkin Procedure for the Numerical Solution of Linear Fcedholm Integral Equations of the Second Kind, In "Mathematical Software II", Informal Proceedings of a Conference, edited by John R Rice. Purdue Oniversity, May 29-31, 1974, p. 238.

7.09 DELVES, L M; WALSH, J (Editors) (1974): Namerieal Solution of Integral Equations, Clarendon Press, Oxford, 339 pp.

7.10 de HOOG, Frank; WEISS, Richard (1974): High order methods for a class of Volterra integral equations with weakly singular kernels, SIAM Journal on Numerical Analysis, Vol. 11, pp. 1166-1180.

7.11 MILLER, G F (1974): Algorithms for Integral Equations, In "Software for Numerical Mathematies", edited by D. J. Evans, Academic Press, London, pp. 139-147.

7.12 NOBLE, B (1977): The Numerical Solution of Integral Equations, In "The State of the Art in Numerical Analysis", edited by D. A. H. Jaeobs, Aeademic Press, London, pp. 915-955.

7.13 SANDERSON, James G (1977): A Numerical comparison of T~o Methods to Solve First Kind Integral Equations, Presented at the SIAM 1977 National Meeting, 13-15 Jtme, Philadelphia, Pennsylvania. Abstract in sIAM Beviw, Vol. 20 (1978), p. 437.

7.7~ SMARZEWSKI, H; MALINOWSKI, H (1978): Numerical Solutions of a Class of Abel Integral Equations, Journal of the Institute of Mathematics and Its Applioatlons, Vol. 22, pp. 159-170.

8. ORDINARY DIFFERENTIAL EQUATIONS

8.01 ALEXAI/DER, Roger (1977): Diagonally Implicit Runge-Kutta Methods for Stiff O.D.E.'s, SIAM Journal on Numerical Analysis, Vol. 14, pp. 1006-1021.

8.02 ALLGOWER, E L; MeCORMICK, S F(1978): Newton's Method wlth Mesh Refinements for Numerical Solution of Nonlinear Two-Point Boundary Value Problems, Numerische Mathematik, Vol. 29, pp. 237-260.

8.03 BARTON, D; WILLERS; I M; ZAHAR, R V M (1971): Taylor Series Methods for Ordinary Differential Equations - An Evaluation, In "Mathe~atlcal Software", edited by John R. Rice, Academic Press, New York, pp. 369-390.

8.0~ BJUREL, Gunnar; DAHLQUIST, Germund; LINDBERG, Bengt; LINDE, avon; ODEN, Lars (1970): Survey of Stiff Ordinary Differential Equations, Report NA 70.11, Department of Information Processing, The Royal Institute of Technology, Stockholm, Sweden.

8.05 BROWN, R Leonard (1978): Evaluation o f Ordinary Differential Equation Software, BIT, Vol. 18, pp. 103-105.

8.06 BOSHARD, Louis B (197b) Subroutine packages for the nomerioal solution of stiff ordinary differential equations, Alliance Research Center Report 8098, The Babeoek~[iloox Company, Alliance Research Center, Ohio, 27 February 1976, 172 pp.

8.07 BYRNE, G D; GEAR, C W; HINDMARSH, A C; HULL, T E; KROGH, F T; SHAMPINE, L F (1975): Panel discussion of quality software for ODEs, In "Numerical Methods for Differential Systems", edited by L Lapidue and W E Schiesser, Academic Press, pp. 267-285.

8.08 BYRNE, George Det al (1977): A comparison of two ODE cgdes: GEAR and EPISODE, Preprint UCRL-79141, January 1977, ~I÷8 p p . , Lawrence Livermore Laboratory. Submitted for publication.

8.09 BYRNE, George Det al : Comparative test results for two ODE solvers-- EPISODE and GEAR, Argonne National Laboratory Report, to appear.

8.10 CASH, ~ R; LI~M, C B (1978): On the computational aspects of semi-implicit Runge-Kutta methods, The Computer Journal, Vol. 21, pp. 363-365.

D~CHICK, R (1977): Error Estimation and Stepsize Control in Maximum Polynomial Degree Nordsieok-Gear Methods, Presented at the SIGNUM Meetiflg on Mathematical Software, 3-4 November 1977, Albuquerque, New Mexico. Abstract in the SIGNUM Newsletter, Vol. 12, No. 4 (Deeember 1977), p. 6.

ENRIGHT, W; BEDET, R; HALL, G; HULL, T; LINOBERG, B (1974): On the Evaluation of Numerical Methods for I/%itial Value Problems in Ordinary Differential Equations, In "Mathematical Software II", Informal Proceedings of a Conference, edited by John R Rice. Purdue University, May ~9-31, 1974, p. 296.

ENRIGHT, W H; HULL, T E; LINDBEEG, B (1975): CompsmlngNumerioal Methods for Stiff Systems of O.D.E:s, BIT, Vol. 15, pp. 10-48.

8.1h ENRIGBT, W H; BULL, T E (1975): Test Results on Initial Value Methods for Non-Stiff Ordinary Differential Equations, SIAM Journal on Numerical Analysis, Vol. 13, pp. 944-961.

8.15 ENEIGHT, W H; BOLL, T E (1975): Comparing numerical methods for the solution of stiff systems of ODEs arising in chemistry, In "Numeriual Methods for Differential Systems", edited by L Lapidus and W E Sehiesser, Academin Press, pp. 45-66.

8.16 ENRIGHT, W H (1978): Improving the Efficiency of Matrix Operations in the Numerical Solution of Stiff Ordinary Differential Equations, ACM Transactions on Mathematical Software, Vol. 4, pp. 127-136.

8;17 ENBIGHT, Wayne H (1979): Using a testing paekage for the automatic assessment of numerical methods'for o.d.e.°a, in "Performance Evaluation of Numerical Software", Proceedings of the IFIP TC 2 Working Conference held in Baden, Austria ' 11-15 Deeember 1978, edited by Lloyd D. Fosdiok, to be published by North-Holland, Amsterdam.

8.18 FLAHERTY, Joseph E; O'MALLEY Jr, R E (1977): The N~merioal Solution of Boundary Value Problems for Stiff Differential Equations, Mathematics of Computation, Vol. 31, pp. 56-93.

8.19 FOX, P A (1971): DESUB: InteETation of a First-Order System of Ordinary Differential Equations, In "Mathematieal Software", edited by John R. Rice, Academic Press, New York, pp. 477-507.

8.20 FOX, Phyllis (1~72): A Comparative Study of Computer Programs for Integrating Differential Equations, Communications of the ACM, Vol. 15, pp. 949-951.

8.21 GEAR, William (1971): Numerical Initial Value Problems in Ordinary Differential Equations, Prentice-Hall, Englewood Cliffs, N.J., 253 pp.

8.22 GEAR, C W (1971): Experience and Problems with the Software for the Automatic Solution of Ordinary Differential Equations, In "Mathematical Softuare", edited by John R. Rice, Academic Press, New York, pp. 211-227.

8.23 GLADWELL, Ian (197~): Testing Ordinary Differential Equation Initial Value Solvers with Implications for Library Soutinea, Presented at the SIAM 1978 Spring Meeting, 24-25 May 1978, Madison, Wisconsin. Reports to appear from the University of Manchester.

8.24 GUDERLEY, Karl G (1975): A umified view of some methods for stiff two-point boundary value problems, SIAM Review, Vol. 17, PP. qIo-442.

8.11

8.12

8.13


8.25 HILL, D R (197b): On eomparing Adams and natural spline multistep formulas, Mathematics of Computation, Vol. 29, pp. 7,1-745.

8.26 HINDMARSH, A C (197b): Note on the Startup of ODE Solvers, SIGNL~4 Newsletter, Vol. 11, No. 4 (December 197b), pp. 12-13.

8.27 de HOOG, Frank R; WEISS, Richard (1976): Difference methods for boundary value problems with a singularity of the first kind, SIAM Journal on Numerical Analysis, Vol. 13, pp. 775-813.

8.28 van der HOUWEN, Peter J; VERWER, d G 41979): Comparison of algorithms for systems of o.d.e.'s originating from parabolic initial boundary value problems in two dimensions, in "Performanoe Evaluation of Numerloal Software", Proceedings of the IFIP TC 2 Working Conference held in Baden, Austria, 11-15 December 1975, edited by Lloyd D. Foadick, to be published by North-Holland, Amsterdam.

8.29 HULL, T E (197,): lhe Development of Software for Solving Ordinary Differential Equations, in Lecture Notes in Mathematics, Vol. 353, Conferenee on the Numerical Solution of Differential Equations, Dundee, 1973. Springer-Verlag, Berlin, pp. 55-63.

8.30 HULL, T E; ENRIGHT, W H; FELLEN, B M; SEDGWICK, A E (197z): Comparing Numerical Methods for Ordinary Differential Equations, SEAM Journal on Numerloal Analysis, Vol. 9, pp. bO3-b37, errata in Vol. 11 (1974), p. b81.

8.31 INGRAM, H L (1973): A comparison of digital computer programs for the numerical solution of ordinary differential equations, NASA Tech. Memo X-b4781, Marshall Space Flight Center, Alabama.

8.32 JACKSON, K R; ENRIGHT, W H; HULL, T E (1978): A Theoretical Criterion for Comparing Runge-Kutta Formulas, SIAM Journal on Numerical Analysis, Vol. 15, pp. b18-641.

8.33 JAIN, M K; SALDANHA, d S V (197~): Higher Order Difference Methods for Second order Two-Point Boundary-Value Problems, Journal of Computational and Applied Mathematics, Vol. g, pp. 199-206.

8.3~ JELTSCH, golf (1977): Multistep Methods Using Higher Derivatives and Damping at Infinity, Mathematics of Computation, Vol. 31, pp. 124-138.

8.35 JOHNSON, A I; BARNEY, J R (197b): Numerical solution of large systems of stiff ordinary differential equations in a modular simulation framework, In "Numerical Methods for Differential Systems", edited by L Lapidus and W E Sehiesser, Academic Press,' pp. 97-124 .

8.36 KEMP, P (197,): Mathematical Software for Ordinary Differential Equations: Chebyshev Series Methods, In "Mathematical Software II", Informal Proceedings of a Conference, edited by John R Rice. Purdue University, May 29-31, 1974, p. 289.

8.37 KROGH, Fred T (197Z): Opinions on Matterm Connected with the Evaluation of Programs and Methods for Integrating Ordinary Differential Equations, SIGN~4 Newsletter, Vol. 7, No. 3, October 197~, pp. 27-48.

8.38 KROGH, F T (1973): On Testing a Subroutine for the Numerical Solution of Ordinary Differential Equations, Journal of the Association for Computing Machinery, Vol. 20, pp. 545-562.

8.39 KROGH, Fred T (1978): Report on the ODE Workshop, 4-5 November 1977, Albuquerque, New Mexico. SIGNUM Newsletter, Vol. 13, No. 2 (June 1978), pp. b-E.

8.40 LAMBERT, J D (1977): The Initial Value Problem for Ordinary Differential Equations, In "The State of the Art in Numerical Analysis", edited by D. A. H. Jacobs, Academic Press, London, pp. 451-500.

8.41 LENTINX, M; FEEEYRA, V (1977): An Adaptive Finite Differenee Solver For Nonlinear Two-Point Boundary Problems with Mild Boundary Layers, SIAM Journal on Numerical Analysis, Vol. 14, pp. 91-111.

8.~2 LINDBERG, BonEr (1977): Characterization of Optimal Stepsize Sequences for Methods for Stiff Differential Equations, SIAM Journal on Numerieal Analysis, Vol. 14, pp. 859-887.

8.h3 OPPELSTRUP, Jesper 41973): Integrationsmetoder ftr ordin~ra differentialekvationer (Integration Methods for Ordinary Differential Equations, in Swedish), ITM Working Paper No. 5, The Swedish Institute of Applied Mathematics, Stockholm, Sweden.

8.~ O'SHEA, Brendan B (1975): Algorithms for the solution of systems of coupled second order ordinary differential equations, Journal of Computational and Applied Mathematics, Vol. 4, pp. 11-17.

8.h5 RENTROP, P (1979): A Taylor Series Method for the Numerical Solution of Two-Point Boundary Value Problems, Numerische Mathematik, Vol. 31, pp. 359-375.

8.46 RUSSEL, Robert D (1977): A Comparison of Collocation and Finite Differences for Two-Point Boundary Value Problems, SIAM Journal on Numerical Analysis, Vol. 14, pp. 19-39.

8.~7 SACKS-DAVIS, R (1977): Error Estimates for a Stiff Differential Eqnation Procedure, Mathematics of Computation, Vol. 31, pp. 939-953.

8.48 SCOTT, M R; WATTS, H A (197b): A systematized eollection of codes for solving two-point boundary-value problems, In "Numerical Methods for Dift'erential Systems", edited by L Lapidus and W E Sehiesser, Academic Press, pp. 197-227.

8.49 SCOTT, Melvin R; WATTS, Herman A 41977): Computational Solution of Linear Two-Point Boundary Value Problems via Orthonormalizetion, SIAM Journal on Numerloal Analysis, Vol. 14, pp. 40-70.

~.50 SHAMPINE, L F; GORDON, M K (1975): Computer Solution of Ordinary Differential Equations, The Initial Value Problem, W H Freeman and Co, San Francisco.

8.51 SHAMPINE, L F (197b): The Quality of Runge-Kutta Formulas, Presented at the SIAM 1976 National Meeting, Ib-18 June, Chicago, Illinois. Abstraet in SIAM Review, Vol. 19 (1977), pp. 395-398.

8.52 SHAMPINE, L F; WATTS, H A (197o): Global Error Estimation for Ordinary Differential Equations, ACM Transactions on Mathematical Software, Vol. 2, pp. 172-18b.

8.53 S~AMPINE, L F; WATTS, H A; DAVENPORT, S M (197b): Solving Nonst£ff Ordinary Differential Equations - the State of the Art, SIAM Review, Vol. 18, pp. 37b-411.

8.5~ SHAMPINE, L F; WATTS, H A (197Y): The Art of Writing a Runge-Kutta Code, Part I, In "Mathematical Software III", edited by John R. Rice, Academic Press, New York, pp. 257-275.

8.55 SHAMPINE, Lawrence F (197~): Stability Properties of Adams Codes, ACM Transactions on Mathematical Software, Vol. 4, pp. 323-329.

8.56 SHAMPINE, L F; GEAR, C W (1979): A User's View of Solving Stiff Ordinary Differential Equations, SIAM Review, Vol. 21, pp; 1-17.

8.57 SILVER, A; SULLIVAN, E (197,): The Numerical Solution of Ordinary Differential Equtions by the Taylor Series Method, In "Mathematical Software IX", Informal Proeeedings of a Conference, edited by John R Rice. Purdue University, May 29-31, 1974, p. 293.

8.58 SINCOVEC, R F (1977): On the Relative Effieiency of Higher Order Collocation Methods for Solving Two-Point Boundary Value Problems, SIAM Journal on Numerical Analysis, Vol. 14, pp. 112-123.

8.59 SKEEL, Robert D; KONG, Antony K (1977): Blended Linear Multistep Methods, ACM Transactions on Mathematical Software, Vol. 3, PP. 32b-345.

8.60 STETTER, H J (197~): On the Maximal Order in PC-Codes, Computing, Vol. 20, pp. 273-280.

8.61 STETTER, Hans J 41979): Performance evaluation of o.d.e, software through modelling, in "Performance Evaluation of Numerical Software", Proceedings of the IFIP TC 2 Working Con ferenee held in Baden, Austria, 11-15 December 197~, edited by Lloyd D. Fosdiek, to be published by North-Holland, Amsterdam.


8.62 TENDLER, Joel M; BICKART, Theodore A; PICEL, Zdenek (1978): A Stiffly Stable Integration Process Using Cyclic Composite Methods, ACM Transactions on Mathematical Software, Vol. 4, pp. 339-368.

8.63 THIELE, F (1975): Accurate Numerical Solutions of Boundary Layer Flows by the Finite-Difference Method of Hermitian Type, Journal of Computational Physics, Vol. 27, pp. 13~-159.

8.64 THOMPSON, S; BUSHARD, L D (197b): A Comparison of Available Software for the Numerical Solution of Stiff Ordinary Differential Equations, Presented at the SIAM 1976 National Meeting, Ib-I~ Ju~e, Chicago, Illinois. Abstract in SIAM Review, Vol. 19 (1977), p. 39~.

8.65 WEENER, J H L1975): Explicit Runge-Kutta Methods with Estimates of the Local Truncation Error, SIAM Journal on Numerical Analysis, Vol. 15, pp. 772-790.

8.66 NALSH, Joan (1974J: Initial and boundary value routines for ordinary differential equations, In "Software fo r Numerical ~athematics", edited by D. J. Evans, Academic Press, London, pp. 177-189.

8.67 WALSH, J (197"1~: Boundary-Value Problems in Ordinary Dif1~rential Equations, In "The State of the Art in Numerical Analysis", edited by D1A. H. Jaeobs, Academic Press, London, pp. 501-533-

8.68 WATANABE, Daniel S (1975): Block Implicit One-Step Methods, Mathematics of Computation, Vol. 32, pp. 405-414.

8.69 YU, T (197H): Comparison of Numerical Methods for Ordinary Differential Equations, Technical Report CNA-73, Center for Numerical Analysis, University of Texas at Austin.

9. PARTIAL DIFFERENTIAL EQUATIONS

9.01 AXELSSON, Owe (197G): A class of iterative methods for finite element equations, Computer Methods in Applied Mechanics and Engineering, Vol. 9, No. 2, pp. 123-137.

9.02 AXELSSON, Owe; N~VERT, Uno (1977): On a Graphical Package for Nonlinear Partial Differential Equation Problems, In "Information Processing 77", Proceedings of the IFIP Congress 1977, Edited by B. Gilehrist, North-Holland Publishing Company, Amsterdam, pp. 103-108.

9.03 BANEGA3, Alexandra (197~J: Fast Poisson Solvers for Problems with Sparsity, Mathematics of Computation, Vol. 32, pp. 441-44G.

9.04 BOISVERT, R F; HOUSTIS, E N; RICE, J R (1975): A System for Performance Evaluation of Partial Differential Equations Software, Report CSD-TR 27~, Department of Computer Science, Purdue University, Lafayette, Indiana 47907.

9.05 BUZBEE, B L; GOLUB, G H; HOWELL, J A (1977): Veetorization for the CRAY-1 of Some Methods for Solving Elliptic Difference Equations,.In "High Speed Computer and AiEorithm Organization", edited by David J. Kuok, Duncan H. Lawrie, and Abmed H. Sameh, Academic Press, New York 1977, pp. 255-271.

9.06 CARVER, M B; HINDS, H W (1977): The Method of Lines and the Advective Equation, Presented at the SIGNgM Meeting on Mathematical Software, 3-4 November 1977, Albuquerque, New Mexico. Abstract in the SIGNDM Newsletter, Vol. 12, No. 4 (December 1977), pp. 9-10.

9.07 CASH, J R (1975): High Order Methods for the Numerical Integration of Ordinary Differential Equations, Numerisohe Mathematik, V@I. 30, pp. 385-409.

9.08 CHANCE, M S; GREENE, J M; GRIMM, R C; JOHNSON, J L; MANICKAM, J; KEENER, N; BERGER, D; BERNARD, L C; GRUBER, R; TROYON, F (1978): Comparative Numerical Studies of Ideal Magnetohydrodynamic Instabilities, Journal of Computational Physics, Vol. 28, pp. 1-13.

9.09 CHANDRA, R; EISENSTAT, S C; SCHULTZ, M H (1975): Conjugate Gradient Methods for Partial Differential Equations, In "Advances in Computer Methods for Partial Differential Equations", Proceedings of the AICA International Symposium on Computer Methods for Partial Differential Equations held at Lehigh University - Bethlehem, Pennsylvania, U.S.A. 17-19 June 1975. Edited by R. Vicbnevetsky, Available from AICA, Rutgers University, Department of Computer Science, New Brunswick, Hew Jersey 05903, pp. tO-04.

9.10 CHANDRA, R; EISENSTAT, S C; SCHULTZ, M H (1977): The Modified Conjugate Resldual Method for Partial Differential Equations, in "Advances in Computer Methods for Partial Differential Equations-II", Proceedings of the second IMACS(AICA) International Symposium on Computer Methods for Partial Differential Equations held at Lehigh University - Bethlehem, Pennsylvania, U.S.A. 22-24 Jane 1977. Edited by R. Viohnevetsky, Available from AICA, Rutgers University, Department of Computer Science, New Brunswick, New Jersey 08903, pp. 13-19.

9.11 CHANG, P N; FINLAYSON, B A (1977): Orthogonal Collocation on Finite Elements for Elliptic Equations, In "Advances in Computer Methods for Partial Differential Equations-IX", Proceedings of the second IMACS(AICA] International Symposium on Computer Methods for Partial Differential Equations held at Lehigh University - Bethlehem, Pennsylvania, U.S.A. 22-24 June 1977. Edited by R. Vichnevetsky, Available from AICA, Rutgers University, Department of Computer Science, New Brunswick, New Jersey 08903, pp. 79-86.

9.12 CHONG, T H (1975): A Variable Mesh Finite Difference Method for Solving a Class of Parabolic Differential Equations in One Space Variable, SIAM Journal on Numerical Analysis, Vol. 15, pp. 835-857.

9.13 CIMENT, Melvyn; LEVENTHAL, Stephen H; WEINBERG, Bernhard C (1975): The Operator Compact Implicit Method for Parabolic Equations, Journal of Computational Physics, Vol. 28, pp. 135-Ibb.

9.14 CONCHS, P; GOLUB, G H; O'LEAHY, D P (1975): Numerical Solution of Nonlinear Elliptic Partial Differential Equations by a Generalized Conjugate Gradient Method, Computing, Vol. 19, pp. 321-339.

9.15 DIETRICH, D; McDONALD, B E; WAEN-VARNAS, A (197b): Optimized Block-Implicit Relaxation, In "Advances in Computer Methods for Partial Differential Equations", Proceedings of the AICA International Symposium on Computer Methods for Partial Differential" Equations held at Lehigh University - Bethlehem, Pennsylvania, U.S.A. 17-19 June 1975. Edited by R. Vichnevetsk~, Available from AICA, Rutgers University, Department of Computer Science, New Brunswick, New Jersey 08903, p. 59.

9.16 FROIEH, Mats (197b;: FroEramsystem f~r FEM-analys, in "Finita Elementmetoden, en datoranpassad ber~kningsmetod ftr inEenJtrsproblem", edited by Nils Erik Wiberg, LiberL~romede!, Lund, pp. g09-424 kin Swedish).

9.17 GARY, John (1975): Comparison of Some Fourth Order Difference Schemes for Hyperbolic Problems, In "Advances in Computer Methods for Partial Differential Equations", Proceedings of the AICA International Symposium on Computer Methods for Partial Differential Equations held at Lehigh University - Bethlehem, Pennsylvania, U.S.A. 17-19 June 1975. Edited by E. Viehnevetsky, Available from AICA, Rutgars University, Department of Computer Science, New Brunswick, New Jersey 08903, pp. 14-Ib.

9.18 GIROUX, E Dick (1977): A Large Mathematical Model Implementation on the STAR-IO0 Computers, In "High Speed Computer and Algorit~m Organization", edited by David J. Kuck, Duncan H. Lawrie, and Ahme~ H. Sameh, Academic Press, New York 1977, pp. 287-298.

9.19 GOTTLIEB, David; TURKEL, Eli (1975): Boundary Conditions for Multistep Finite-Difference Methods for Time-Dependent Equations, Journal of Computational Physics, Vol. 2b, pp. 181-196.

9.20 GROOMS, David W (IgTI): Integration of Partial Differential Equations, A Bibliography with Abstracts, NTIS/PS-77/0590, National Technical Information Service, Springfield, Vs. 22161.


9.21 HACKBUSCH, W (197~): On the Multi-Grid Method Applied to Difference Equations, Computing, Vol. 20, pp. 291-30b.

9.22 HICKS, D L; MADSEN, M M (1970): An Accuracy Property of Certain Hyperbolic Difference Schemes, Sandia Laboratories, SAND-7b-0389, Albuquerque , New Mexico.

9.23 HOPKINS, T R; WAIT, R (1975): A comparison of numerical methods for the solution of quasilinear partial differential equations, Computer Methods in Applied Mechanics and Engineering, Vol. 9, PP. 181-190.

9.24 HOUSTIS, E N; LYNCH, R E; PAPATHEODOROU, T S; RICE, J R (197b): Development, Evaluation and Selection of Methods for Partial Differential Equations, In "Advances in Computer Methods' for Partial Differential Equations" , Proeeedings of the AICA International Symposium on Computer Methods for Partial Differential Equations held at Lehigh University - Bethlehem, Pennsylvania, U.S.A. 17-19 June 1975. Edited-by R. Viehnevetsky, Available from AICA, Hutgers University, Department of Computer Scienne, New Brunswick, New Jersey 05903, pp. I-o.

9.25 HOUSTIS, E N; RICE, J R (197"[): Software for Linear Elliptic Problems on General Two Dimensional Domains, In "Advances in Computer Methods for Partial Differential Equations-II-, Proceedings of the second IMACS(AICA) International Symposium on Computer Methods for Partial Differential Equations held at Lehigh University - Bethlehem, Pennsylvania, U.S.A. 22-24 June 1977. Edited by R. Viohnevetsky, Available from AICA, Rutgers University, Department of Computer Science, New Brunswick; New Jersey 05903, pp. 7-12.

9.26 HOUSTIS, E N; PAPATHEODOROU, T S (1977): Comparison of Fast Direct Methods for Elliptic Problems, In "Advances in Computer Methods for Partial Differential Equations-If", Proceedings of the second IMACS(AICA) International Symposium on Computer Methods for Partial Differential Equations held at Lehigh University - Bethlehem, Pennsylvania, U.S.A. 22-24 June 1977. Edited by R. Vichnevetsky, Available from AICA, Rutgers University, Department of Computer Science, New Brunswick, New Jersey 08903, pp. 4b-52.

9.27 HOUSTIS, E N; LYNCH, R E; RICE, J R; PAPATHEODOROU, T S (1975): Evaluation of Numerical Methods for Elliptic Partial Differential Equations, Journal of Computational Physics, Vol. 27, pp. 323-350.

9.28 HOUSTIS, E N (1975): Collocation Methods for Linear Elliptic Problems, BIT, Vol. 18, pp. 301-310.

9.29 HOUSTIS, E N (1975): The Complexity of Numerical Methods for Elliptic Partial Differential Equations, Journal of Computational and Applied Mathematics, Vol. 4, pp. 191-197.

9.30 JEZERNIK, A; LEECH, A (1973): The Comparison of Iterative and Direet Solution Techniques in the Analysis of Time-Dependent Stress Problems! Including Creep, by the Finite Element Method, In "The Mathematics of Finite Elements and Applications", Proceedings of the Brunel University conference in April 197Z, edited by J. H. Whiteman, Academic Press, London and New York, pp. 449-4b2.

9.31 KENDALL, Richard P; WHEELER, Mary F (197b): A Crank-Nicolson-H-I-GALEREIN Procedure fop Parabolic Problems in a Single-Space Variable, SIAM Journal on Numerical Analysis, Vol. 13, pp. 8b1-~7b.

9.32 KINCAID, David R; YOUNG, David M (1977): ITPACK - Codes for Solving Large Sparse Linear Systems by Iterative Methods: Preliminary Report, In "Advances in Computer Methods for Partial Differential Equations-II", Proceedings of the second IMACS(AICA) International Symposium on Computer Methods for Partial Differential Equations held at Lehigh University - Bethlehem, Pennsylvania, U.S.A. 22-24 June 1977. Edited by R. Vichnevetsky, Available from AICA, Rutgers University, Department of Computer Science, New Brunswick, New Jersey 08903, p. 133.

9.33 LAWSON, J D; MORRIS, J L1 (1978): The Extrapolation of Fist Order Methods for Parabolic Partial Differential Equations. I, SIAM Journal on Numerical Analysis, Vol. 15, pp. 1212-1224.

9.3~ LYNCH, Robert E; RICE, JohnR,(1975): High accuracy finite difference approximation to solutions of elliptic partial differential equations, Proceedings of the National Academy of Sciences, Vol. 75, No. 6, pp. 2541-2544.

9.35 LYNCH, R E; RICE, J R (1975): The HODIE Method and i~s Performance, in "Recent Advances in Numerical Analysis", Edited by Carl de Boor, Academic Press,. New York, pp. 1~3-175.

9.36 MADSEN, Niel K (197b): Numerical Results Using Collocation Methods for Partial Differential Equations, Presented at the SIAM 1976 National Meeting, Ib-18 June, Chicago, Illinois. Abstract in SIAM Review, Vol. 19 (1977), p. 3H9.

9.3~ MADSEN, Niel K; SINCOVEC, Richard F (197b): General Software for Partial Differential Equations, In "Numerical Methods for Differential Systems", edited by L Lapidus and W E Schiesser, Academic Press, pp. 229-242.

9.38 MAJDA, Andrew; McDONOUGR, James; OSHER, Stanley (1975): The Fourier Method for Nonsmooth Initial Data, Mathematics of Computation, Vol. 32, pp. 1041-1081.

9.39 MELGAAED, D K (197@): PDETWO: General Software for Two-dimensional Partial Differential Equations, Presented at the SIAM 1976 National Meeting, I@-18 June, Chicago, Illinois. Abstract in SIAM Review, Vol. 19 (1977), pp. 389-390.

9.40 ORTEGA, James M; VOIGT, Robert G (1977): Solution of Partial Differential Equations on Vector Computers, In the Proceedings of the 1977 Numerical Analysis and Computers Conference, 30-31 March, Madison, Wisconsin. ARC Report 77-3, U S Army Research Office, Research Triangle Park, North Carolina, pp. 475-525.

9.41 POLAK, S d; 3CHROOTEN, J; BINKHUYSEN, C Barneveld (1978): TEDDY2, A Program Package for Parabolie Composite Region Problems, ACM Transactions on Mathematical Software, Vol. 4, pp. 209-227.

9.~2 PROSKUROWSKI, W (1975): On the Numerical Solution of the Eigenvalue Problem of the Laplace Operator by a Capacitance Matrix Method, Computing, Vol. 20, pp. 139-151.

9.43 RICE, John R (197o): Algorithmic Progress in Solving Partial Differential Equations, SIGNUM Newsletter, Vol. 11, No. 4 (December 197b), pP- b-10.

9.44 RICE, John R (1977): ELLPACK: A Research Tool for Elliptic Partial Differential Equations Software, In "Mathematical Software IIl", edited by John R. Rice, Academic Press, New York, pp. 319-341.

9.45 ROACHE, Patrick J (1975~: Recent Developments and Problem Areas in Computational Fluid Dynamics, In "Computational Meshanics", edited by J. T. eden, Proceedings of the International Conference on Computational Methods in Nonlinear Mechanics, Austin, Texas, 1974. Lecture Notes'in Mathematics, Vol. 461, Springer-Verlag, Berlin-Heidelberg-New York, pp. 195-258.

9.46 SEITELMAN, L H (1973): Soma Practical Solution Techniques for Finite Element Analysis, In "The Mathematics of Finite Elements and Applications", Proceedings of the Brunel University conference in April 197Z, edited by J. R. Whiteman, Academic Press, London and New York, pp. 471-481.

9.47 SHIEH, A S L (1979): Fast Poisson Solvers on General Two Dimensional Regions for the Dirichlet Problem, Numerisohe Mathematik, Vol. 31, pp. 405-429.

9.48 SINCOVEC, R F; MADSEN, N K (197b): PDECOL: A Collocation Package for Solving Partial Diffemential Equations, Freprint UCRL-782b3 (Roy.l, July 1977), Presented at the SIAM 1976 National Meeting, Ib-1~ June, Chicago, Illinois. Abstract in SIAM Review, Vol. 19 (1977), pp. 39b-397.

Journal of Computational and Applied Mathematics, volume 5, no 2, 1979. i58

9.~9 SINGH, KamaP J (1977J: Improved Accuracy of Finite . Element Solution by a New Reduced Integration Method, In "Advances in Computer Methods for Partial Differential Equatlons-II,,, Proceedings of the second IMACS(AICA) International Symposium on Computer Methods for Partial Differential Equations held at Lehigh University - Bethlehem, Pennsylvania, U.S.A. 22-24 June 1977. Edited by R. ¥ichnevetsky, Available from AICA, Rutgers University, Department of Computer Science, New Brunswick, New Jersey 08903, pp. b7-73.

9.50 SOD, Gary A (197~): A S u r v e y o f Several Finite Difference.Methods for Sys tems of Nonlinear Hyperbolic Conservation Laws, Journal of Computational Physics, Vol. 27, pp. 1-31.

9.51 SQUIRE, William; TRAFP, George (1975): Solution of Partial Dif1~rentlal Equations by Numerical Inversion of the Laplace Transform, In "Advances in Computer Methods for Partial Differential Equations", Proceedings of the AICA International symposium on Computer Methods for Partial Differential Equations held at Lehigh University - Bethlehem, Pennsylvania, U.S.A. 17-19 June 1975. Edited by R. ~iohnevetsky, Available from AICA, Rutgers UnivErsity, Department of Computer Science, New Brunswick, New Jersey 08903, pp. 75-79.

9.52 SWARTZ, Blair (1975): Comparing Certain Classes of Difference and Finite Element Methods for a Hyperbolic Problem, In "Advances in Computer Methods fop Partial Differential Equations", Proceedings of the AICA International Symposium on Computer Methods for Partial Differential Equations held at Lehigh University - Bethlehem, Pennsylvania, U.S.A. 17-19 June 1975. Edited by R. Viohnevetsky, Available from AIOA, Rutgers University, Department of Computer Science, New Brunswick, New Jersey 0~903, pp. 17-19.

9.53 TUANN, Shih-Yu; OLSON, Mervyn D (197~): Review of Computing Methods for Reeiroulating Flows, Journal of Computational Physics, Vol. 29, pp. 1-19..

9.5~ TURKEL, Eli (1977J: Composite Methods for Hyperbolic Equations, SIAM Journal on Numerical Analysis, Vol. 14, pp. 74~-759.

9.55 TURKEL, Eli (197~): Extrapolation Methods for Dynamic Partial Differential Equations, Numsrisohe Mathematik, Vol. 29, pp. 269-285.

9.56 TYLER, L D (1971): Heuristic Analysis of Convective Finite Difference Temhniques, In "Proceedings of the Second International Conference on Numerical Methods in Flui~ Mechanics", 15-19 September 1970, University of California, Berkeley. Edited by Maurice Holt. Lecture Notes in Physics, Vol 8, Springem-Verlag, Berlln-Heidelberg-New York," pp. 314-334.

9.57 WILHEI24SON, Robert B; EEICESEN, dames H (1977): Direct Solutions for Poisson's Equation in Three Dimensions, Journal of Computational Physics, Vol. 25, pp. 319-331.

9.58 YOUNG, David M (197b): Iterative Solution of Linear and Nonlinear Systems Derived f rom Elliptic Partial Differential Equations, In "Computational Mechanics", edited by J. T. Oden, Proceedings of the International Conference on Computational Methods in Nonlinear Mechanics, Austin, Texas, 1974. Lecture Notes ~n Mathematics, Vol. 451, Springer-Verlag, Berlin-Heidelberg-New York, pp. 255-295.


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