Charles W. Groetsch,Citadel Distinguished Professor of Mathematical ScienceOffice: (843) 953-5036 fax: (843) 953-7391e-mail: charles.groetsch@citadel.edu

Vitae updated November, 2011

EDUCATION

B.S., M.S., University of New Orleans; Ph.D. Louisiana State University

EXPERIENCE

Associate Engineer, Applied Mathematics Department, Space Division, Launch Systems Branch, Boeing Company, 1966-68Visiting Assistant Professor of Mathematics, University of Rhode Island, 1974-75Assistant Professor, University of Cincinnati, 1971-75Consultant, Management Decisions Development Corp., Cincinnati, 1976-82Director of Graduate Studies, Mathematics Dept., Univ. of Cincinnati, 1975-79Associate Professor, University of Cincinnati, 1976-81Research Associate, USAF Flight Dynamics Laboratory, Summer, 1978Senior Visiting Fellow, University of Manchester, England, Summer and Fall,1980Professor of Mathematics, University of Cincinnati, 1981-2006Gastprofessor, Universität Kaiserslautern, Germany, Spring, 1983Head, Department of Mathematical Sciences, University of Cincinnati, l985 - 90Visiting Fellow, Centre for Mathematical Analysis, Australian National University, Summer, l986Visiting Member, Forschungsinstitut für Mathematik, ETH-Zurich, Switzerland, Fall, 1990.Raybould Research Fellow, University of Queensland, Australia, Winter, 1996Interim Dean, McMicken College of Arts and Sciences, University of Cincinnati, 2000-2001Traubert Chair and Dean, School of Science and Mathematics, The Citadel, 2006-2011Distinguished Professor of Mathematical Science, The Citadel, 2011-

ACTIVITIES

Editorial Boards: Co-Editor: Journal of Integral Equations & Applications, 2002-08Associate Editor: Numerical Functional Analysis and Optimization, 1986-, SIAM Review 1992-96, Electronic Journal of Differential Equations, 1992-,

Journal of Integral Equations & Applications, 1994-2008, 2009 - Journal of Mathematical Analysis & Applications, 1996-2005

International Journal of Pure and Applied Mathematics, 2000-Electronic Journal of Mathematical and Physical Sciences, 2002 – Advisory Board, Scientific Journals International, 2008 -

Referee: For approximately 70 journals in mathematics, physics, computing, and engineering. Reviewer: SIAM Review, Mathematical Reviews, Computing Reviews, Zentralblatt für Mathematik, Zeitschrift für Angewandte Mathematik und Mechanik, Mathematics of Computation.

Organizer: U.C. Symposium on Numerical Analysis, May, l979 (co-organized with J. T. King) MAA (Ohio) Special Session on Approximations and Numerical Methods, Spring, 1984 Alpine-U.S. Seminar on Inverse and Ill-posed Problems, St. Wolfgang, Austria, June, l986 (co-organized with H. W. Engl) CBMS Regional Conference on Fractal Geometry, Cincinnati, August, l987 (co-organized with K.R. Meyer)

NSF Faculty Enhancement Workshop on the Mathematics of Inverse Problems, Cincinnati, June,1992

MAA (Ohio) Special Session on Inverse Problems in the Undergraduate Curriculum, Ohio Northern University, Fall, 1993 MAA Minicourse on Inverse Problems in the Classroom, 100th Annual Meeting AMS, Cincinnati, January, 1994 Workshop on Ill-posed Problems for Graduate Students, Cincinnati, June, 1994 (Co-organizer with D. Murio and T. King)

MAA (Ohio) Spring sectional meeting, University of Cincinnati, March, 2004

Chair: Institute for Mathematics and Its Applications Conference Selection Committee, 1988-89. MAA George Polya Award Committee, 1995-98.

Member: Organizing Committee, IMA Industry Day, University of Chicago, December,1989. Presidential Young Investigator Panel, National Science Foundation, Washington, D.C., 1989. Committee of Visitors, Division of Mathematical Sciences, National Science Foundation, Washington, D.C., 1990 Mathematical Association of America Consultant, 1991-95

National Research Council Department Chairs Panel on Implementation of the David II Report, 1990

SIAM Visiting Lecturers Program, 1995-

Joint Policy Board on Mathematics, Taskforce on Educational Activities of Faculty, 1995-99MAA Visiting Lecturer, 1999-2004National Advisory Committee, AASCU Project on Improving Mathematics Instruction for Teachers, 2000-2003

FELLOWSHIPS AND GRANTS (PI=Principal Investigator, CPI=Co-investigator)

Air Force Office of Scientific Research Grant (PI), 1979-80Science Research Council (Great Britain) Grant (CPI), 1980National Science Foundation Grants (PI), l986-87, 1992-94, 1996-2000, (CPI) 2002-05NATO Division of Scientific Affairs Grant (PI), 1993-96Institute for Advanced Study Subcontract (NSF) (PI), 1997-2001, (CPI) 2003-2006OBR - Eisenhower Professional Development Program (PI), 1998-99OBR – Enhancing Teacher Quality Program (PI), 2000-2001

HONORS AND AWARDS

Exchange Scientist, National Academy of Sciences - Akademie der Wissenschaften der DDR, Spring, 1979

McMicken Award for Distinguished Scholarship, University of Cincinnati, 1991 (Inaugural research award among ~400 tenure line faculty)

Fellow of the Graduate School, University of Cincinnati, 1991- (lifetime appointment irrespective of affiliation)

George Pólya Award, Mathematical Association of America, 1994 (national award for expository excellence in mathematics)

Faculty Achievement Award, University of Cincinnati, 1994

Presidential Citation, for “Advancing the application of mathematics to science and industry”, Society for Industrial and Applied Mathematics, 1995

Decanal Citation, Universidad Nacional de Colombia, Sede Medellin, “por la importante contribcion academica a traves del cursillo ‘Problemas Inversos y Teoria de Operadores’”, 1998.

Sigma Pi Sigma (ΣΠΣ National Physics Honor Society, inducted 2011 in recognition of distinguished scholarship in physics)

Two special issues (Vol. 22, Nos. 2,3, 2010) of the Journal of Integral Equations and Applications dedicated by the Editors and authors to Charles Groetsch in recognition of

“high regard for his contributions to the world of mathematics” and his “fundamental contributions to the field of inverse problems.”

Elected a Fellow of the American Association for the Advancement of Science (AAAS), 2010, in recognition of “distinguished contributions of the application of mathematics to science, particularly in the areas of inverse or ill-posed problems, approximation theory, and mathematical modeling.” RESEARCH INTERESTS

Inverse and ill-posed problems, Integral Equations of the First Kind, Numerical Analysis, Approximation Theory, Applied Mathematics, Mathematics Pedagogy

PhD DISSERTATIONS SUPERVISED (All at University of Cincinnati)

B. J. Jacobs, Topics in the approximation of generalized inverses, Ph.D., 1977.Currently Honeywell Fellow (retired).J. Guacaneme Dix, Aspects of the theory of Tikhonov's method for the numericalsolution of integral equations, Ph.D., 1984. Currently Professor of Mathematics, Texas State University.G.D. Callon, Theory and approximation of the restricted pseudosolution, Ph.D.,l986. Currently Professor of Mathematics, Franklin College.

INVITED LECTURES AT INTERNATIONAL SYMPOSIA (Local Sponsor in parentheses)

Inverse and Improperly Posed Problems, Halle, E. Germany (Akademie derWissenschaften der DDR), June, 1979.

Nonlinear Analysis and Applications, St. Johns, Newfoundland (Canadian National Research Council), June, 1981.

Treatment of Integral Equations by Numerical Methods, Durham, England (LondonMathematical Society), July, 1982.

Improperly Posed Problems and Their Numerical Treatment, Oberwolfach, W. Germany, (Mathematisches Forschungsinstitut-Oberwolfach), October, 1982.

Centro Internazionale Matematico Estivo Conference on Inverse Problems, Montecatini Terme, Italy (Consiglio Nazionale delle Ricerche), June, l986.

Practical Treatment of Integral Equations, Boundary Element Methods and

Singular Equations, Oberwolfach, W. Germany (Mathematisches Forschungsinstitut-Oberwolfach), December, 1988

International Conference on Integral Equations and Inverse Problems,Varna, Bulgaria (Bulgarian Academy of Sciences), September, 1989.

International Symposium on Inverse Problems in Engineering Sciences, Osaka, Japan (Mathematical Society of Japan), August, 1990.

International Conference on Computational Mathematics, Matsuyama, Japan (Ehime University, Japan Society for the Promotion of Science) September, 1990

Workshop on Generalized Inverses, New Delhi, India (Indian Statistical Institute) December, 1992

Second Hellenic-European Conference on Mathematics and Informatics, Athens, Greece (Hellenic Mathematical Society), September, 1994

Third Southern Hemisphere Symposium on Undergraduate Mathematics Teaching, Berg en Dal, South Africa (African Mathematical Union; South African National Research Foundation), July, 2001

AMS/UMI Special Session on History of Mathematics, Pisa, Italy (Unione Matematica Italiana, Istituto Nazionale di Alta Matematica), June, 2002.

Inverse Problems in the Applied Sciences, Sapporo, Japan, (Japanese National Science Foundation), July, 2006

Tenth International Conference on Integral Methods in Science and Engineering, University of Cantabria, Santander, Spain (Ministerio de Educacion y Ciencia, Espana), July , 2008.

First Mexican Symposium on Inverse Problems and Applications, Ixtapa-Zihuatenejo, Mexico (Consejo Nacional de Ciencia y Technologia; Universidad Autónoma Metropolitana-Iztapalapa), January, 2010

COLLOQUIA & MAJOR LECTURESUniversity of Rhode Island, November, 1974Boston University, March, 1975.Brown University, May, 1975.Idaho State University, February, 1976.University of Rhode Island, February, 1976.Air Force Institute of Technology, July, 1978.

Free University of Berlin, May, 1979.Central Institute for Mathematics & Mechanics (E. Berlin), June, 1979.University of Rostock, E. Germany, June, 1979.Syracuse University, November, 1979.University of Manchester, England, November, 1980.Eidgenössische Technische Hochschule, Zurich, December, 1980.Miami University, February, 1981.University of Manchester, England, June, 1982.University of Kaiserslautern, W. Germany, May, l983.University of Frankfurt, W. Germany, May, 1983.University of Florence, Italy, June, 1983.University of Linz, Austria, June, 1983. Iowa State University, April, l985.Drake University (MAA Iowa Section SIAM Lecture) April, l985.University of Puerto Rico, April, l985.University of Melbourne, Australia, July, l986.LaTrobe University, Australia, July, l986.Centre for Mathematical Analysis, Canberra, Australia, August, l986.Australian National University, August, l986.University of New South Wales, Australia, August, l986.Montana State University, October, l986.Eastern Kentucky University, March, l987.University of Klagenfurt, Austria, March, l987.Wright State University, April,1988.Northern Jiaotong University, Beijing, China, September,1988.Peking University, Beijing, China, September, 1988.Nankai Institute of Mathematics, Tianjin, China, September, 1988.University of Graz, Austria, November, 1990University of Munich, Germany, November, 1990University of Göttingen, Germany, November, 1990.University of Linz, Austria, November, 1990.Eidgenössische Technische Hochschule, Zurich, November, 1990.University of Louisville, April, 1991Ball State University, November, 1991.Eastern Kentucky University, March, 1992.Ball State University, October, 1992.National University of Singapore, December, 1992Ohio Northern University, October, 1993Kent State University, February, 1994Bowling Green State University, April, 1994 University of Karlsruhe, Germany, July, 1994Whitman College, November, 1994Radford University, March, 1995Boston College, September, 1995University of Akron, October, 1995University of Queensland, Australia, January & February, 1996

Colorado School of Mines, March, 1996Rose-Hulman Institute of Technology, March, 1998Universidad Nacional de Colombia, Medellin, September, 1998Western Kentucky University, October, 1998Tennessee Technological University, October, 1998Bowling Green State University, March, 1999Illinois State University, December, 1999University of Kentucky, Lexington, February, 2000Earlham College (IMAA Keynote Address), March, 2000Ball State University, September, 2000Xavier University, November, 2000 .Calvin College, March, 2001Michigan Epsilon Section, Pi Mu Epsilon, March, 2001Western Michigan University, March, 2001University of Tennessee, Knoxville, November, 2001Baker University, February, 2002Defiance College, March, 2002Annual meeting of the Pacific Northwest Section MAA (Keynote Address), June, 2003Southeastern Louisiana University, October, 2003USMA-West Point, October, 2004Michigan Technological University, October, 2004Xavier University, April, 2005Shawnee State University, May, 2005Northern Kentucky University, February, 2006Hokkaido University, Sapporo, Japan, July, 2006College of Charleston, April, 2007 Northern Michigan University, April, 2008 University of Rhode Island, November, 2008

PUBLICATIONS

Books and Monographs

C.W. Groetsch, Generalized Inverses of Linear Operators: Representation and Approximation, Dekker, New York, 1977. ISBN 0-8247-6615-6

Charles Groetsch, Elements of Applicable Functional Analysis, Dekker, New York, 1980. ISBN 0-8247-6986-4

C.W. Groetsch, The Theory of Tikhonov Regularization for Fredholm Equations of the First Kind, Pitman, London, 1984. ISBN 0-273-08642-1

J. Evans, C. W. Groetsch, and M. Walker, Fundamentals of Calculus: Applications to Managerial, Social and Life Sciences, West, St. Paul, l986. ISBN 0-314-93175-9

J. Evans, C. W. Groetsch, and M. Walker, An Introduction to Calculus: Methods and Applications, West, St. Paul, l986. ISBN 0-314-93176-7

C.W. Groetsch and J. Thomas King, Matrix Methods and Applications, Prentice-Hall, Englewood Cliffs, l988. ISBN 0-13-565565-X

H.W. Engl and C.W. Groetsch (Eds.), Inverse and Ill-Posed Problems, Academic Press,Boston, l987. ISBN 0-12-239040-7

C.W. Groetsch, Inverse Problems in the Mathematical Sciences, Vieweg Verlag, Wiesbaden/Braunschweig, Germany, 1993. ISBN 3-528-06545-1

C.W. Groetsch, Inverse Problems in the Mathematical Sciences - Japanese translation by Kazuei Onishi, Kazumi Tanuma and Masahiro Yamamoto, Saiensu-sha, Tokyo, 1996. (Also appeared as a special edition of the Japanese journal Mathematical Sciences, June , 1996). ISBN 0-547-00619-1

C.W. Groetsch, Inverse Problems, Mathematical Association of America, Washington, D.C., 1999. ISBN 0-88385-716-2

C.W. Groetsch, Inverse Problems – Japanese translation by Akira Kaneko, Science Press, Tokyo, 2002. ISSN 0386-8257.

C.W. Groetsch, Inverse Problems – Mandarin Chinese translation by Jin Cheng, Yongji Tan and Jijun Liu, Springer, Beijing, 2006. Co-published by Tsinghua University Press, Biejing. ISBN 7-302-12713-1

C.W. Groetsch, Stable Approximate Evaluation of Unbounded Operators, LNM1894, Springer-Verlag, Heidelberg and Berlin, Germany, 2007, ISBN 3-540-39942-1

Published Articles (by sub-disciplinary category)

Integral Equations of the First Kind

C.W. Groetsch, Integral equations of the first kind, inverse problems and regularization, Journal of Physics: Conference Series 73(2007) 102001, 32 pp.

C.W. Groetsch, Some integral equations of the first kind in mechanics and regularization of ill-posed operator equations, in Inverse Problems in Engineering Science (M. Yamaguti et al, Eds.), Springer Verlag, Tokyo, 1991, pp.11-29.

C.W. Groetsch, Convergence analysis of a regularized degenerate kernel method for Fredholm integral equations of the first kind, Integral Equations and Operator Theory 13(1990), 67-75

C.W. Groetsch and J. Guacaneme, Arcangeli's method for Fredholm equations of the first kind, Proceedings of the American Mathematical Society, 99(l987), 256-26l.

C.W. Groetsch, Uniform convergence of regularization methods for Fredholm equations of the first kind, Journal of the Australian Mathematical Society 39(1985) 282-286.

C.W. Groetsch and J. Guacaname, On regularized Ritz approximations for Fredholm equations of the first kind, Rocky Mountain Journal of Mathematics 15(l985), 33-39. Also appeared as Publication No. l0, Istituto di Analisi Globale e Applicazioni, CNR, Florence, Italy, l983.

C.W. Groetsch, J.T. King and D.A. Murio, Asymptotic analysis of a finite element method for Fredholm equations of the first kind, Numerical Treatment of Integral Equations (C.T.H. Baker, Ed.) Academic Press, London, 1982, pp. 1-11.

C.W. Groetsch, On a regularization-Ritz method for Fredholm equations of the first kind, Journal of Integral Equations 4 (1982), 1973-182. C.W. Groetsch, On existence criteria and approximation procedures for integral equations of the first kind, Mathematics of Computation 29 (1975), 1105-1108.

Inverse and Ill-posed Problems

C.W. Groetsch, Linear inverse problems, pp. 3-41, Chapter I in Handbook of Mathematical Methods in Imaging (O. Scherzer, Univ. Vienna, Ed.), Springer, New York, 2011.

C.W. Groetsch, Inverse problems: the other two-thirds of the story, Quaestiones Mathematicae 24(2001), Supplement 1, 89-94.

C.W. Groetsch, Regularization and stabilization of inverse problems, Chapter 2 in Handbook of Analytic- Computational Methods in Applied Mathematics, Chapman and Hall, Boca Raton, 2000, pp. 31-64.

C.W. Groetsch, Tartaglia's inverse problem in a resistive medium, The American Mathematical Monthly 103(1996), 546-551.

C.W. Groetsch, Spectral methods for linear inverse problems with unbounded operators, Journal of Approximation Theory 70(1992), 16-28.

C.W. Groetsch and E. Schock, Asymptotic convergence rate for Arcangeli's method for ill-posed problems, Applicable Analysis l8 (l984), l75-l82.

C.W. Groetsch, Comments on Morozov's discrepancy principle, Improperly Posed Problems and their Numerical Treatment (G. Hämmerlin & K. Hoffmann, Eds.), Birkhauser, Basel, 1983, pp. 97-104.

C.W. Groetsch, On the Kryanev-Lardy method for ill-posed problems, Mathematisches Nachrichten 96(1980), 27-31

Regularization Theory

C.W. Groetsch, Tikhonov-Phillips regularization, Encyclopaedia of Mathematics, Supplement II, Kluwer, Dordrecht, 2000, pp. 462-464.

Martin Hanke and C.W. Groetsch, Nonstationary iterated Tikhonov regularization, Journal of Optimization Theory and Applications 98(1998), 37-53.

C.W. Groetsch and M. Hanke, Regularization by projection of unbounded operators arising in inverse problems, in Inverse Problems and Applications to Geophysics, Industry, Medicine and Technology (D.D. Ang, et al., Eds.), pp. 61-70, Publications of the HoChiMinh City Mathematical Society, vol.2, HoChiMinh City, 1995.

C.W. Groetsch and A. Neubauer, Regularization of ill-posed problems: Optimal parameter choice in finite dimensions, Journal of Approximation Theory 58(1989), 184-201.

H.W. Engl and C.W. Groetsch, A higher order approximate method for restricted linear least squares problems, Bulletin of the Australian Mathematical Society 37(l988) l2l-l30.

C.W. Groetsch and C.R. Vogel, Asymptotic theory of filtering for linear operator equations with discrete noisy data, Mathematics of Computation 49 (l987), 499-506.

H.W. Engl and C.W. Groetsch, Projection-regularization methods for linear operator equations of the first kind, Proceedings of the Centre for Mathematical Analysis (Canberra), 17(1988), 17-31.

C.W. Groetsch, Regularization with equality constraints, in Inverse Problems (G. Talenti Ed.) Springer-Verlag, New York, l986, pp. l68-l8l.

C.W. Groetsch, On the asymptotic order of accuracy of Tikhonov regularization, Journal of Optimization Theory and Applications 41 (1983), 293-298.

C.W. Groetsch and J.T. King, The saturation phenomenon for Tikhonov regularization, Journal of the Australian Mathematical Society, (Series A) 35 (1983), 254-262

C.W. Groetsch, On a class of regularization methods, Bolletino della Unione Matematica Italiana, 17 (1980), 1411-1419.

C.W. Groetsch and J.T. King, Extrapolation and the method of regularization for generalized inverses, Journal of Approximation Theory, 25 (1979), 233-248.

C.W. Groetsch, Sequential regularization of ill-posed problems involving unbounded operators, Commentationes Mathematicae Universitatis Carolinae 18, 3 (1977), 489-498.

Numerical Analysis

D.A. French and C.W. Groetsch, Numerical solution of a class of integral equations arising in a biological laboratory procedure, Integral Methods in Science and Engineering, Volume 2, Computational Methods, (C. Constanda and E. Perez, Eds.), pp. 161-171, Birkhäuser, Boston, 2010.

C.W. Groetsch, Regularized product integration for Hadamard finite part integrals, Computers and Mathematics with Applications 30(1995), 129-135.

C.W. Groetsch, A numerical method for some inverse problems in nonlinear heat transfer, Computer Mathematics and Its Applications 1(1994), 49-60.

C.W. Groetsch, The optimal order of accuracy in Vasin's method for differentiation of noisy functions, Journal of Optimization Theory and Applications 74(1992), 373-378.

C.W. Groetsch, A numerical method for the surface temperature of a sphere under nonlinear boundary conditions, Zeitschrift für angewandte Mathematik und Mechanik 74(1994), 142-143.

C.W. Groetsch, A simple numerical model for nonlinear warming of a slab, Journal of Computational and Applied Mathematics 38(1991), 149-156.(Reprinted in Advances in Computational Mathematics, T. Yamamoto, Ed., North Holland, Amsterdam, 1992)

C.W. Groetsch, Differentiation of approximately specified functions, American Mathematical Monthly 98(1991), 847-850.

C.W. Groetsch, Numerical methods for a nonlinear integral equation and an associated inverse problem, Integral Equations and Inverse Problems (R. Lazarov and L. Petkov, Eds.), Pitman, London, 1991, 90-95.

C.W. Groetsch, Remarks on some iterative methods for an integral equation in Fourier optics, Transport Theory, Invariant Imbedding and Integral Equations (P. Nelson et al., Eds.), Marcel Dekker, New York, 1989, pp.313-324..

C.W. Groetsch, Convergence of a numerical algorithm for a nonlinear heat transfer problem, Zeitschrift für angewandte Mathematik & Mechanik, 65 (1985), 645.

C.W. Groetsch, Numerical treatment of a nonlinear problem arising in heat transfer, Proc. Intl. Conf. on Nonlinear Analysis & Applications, St. John's, Newfoundland (S. P. Singh, Ed.) Marcel Dekker, New York, pp. 357-362.

Operator Approximation Theory

C.W. Groetsch, An iterative stabilization method for the evaluation of unbounded operators, Proceedings of the American Mathematical Society 134(2006), 1173-1181.

C.W. Groetsch, Stabilization via projection, Advances in Applied and Computational Mathematics, (F. Liu et al., Eds.), Nova Science Publishers, NY, 2006, pp. 103-112.

C.W. Groetsch, A converse result for the Tikhonov-Morozov method, Integral Methods in Science and Engineering: Theoretical and Practical Aspects, C. Costanda et al., Eds., Birkhaeuser, Boston, 2006, pp. 71-78.

C.W. Groetsch, A finite dimensional variational method for unbounded operators, in Integral Methods in Science and Engineering: Theoretical and Practical Aspects, C. Costanda et al., Eds., Birkhäuser, Boston, 2006, pp. 61-70.

C.W. Groetsch, Dykstra’s algorithm and a representation of the Moore-Penrose inverse, Journal of Approximation Theory 117(2002), 179-184.

C.W. Groetsch, Functional Analysis, Encyclopedia of Physical Science and Technology, Vol. 6, Third Edition, 2002, Academic Press, San Diego, pp. 337-353.

C.W. Groetsch and Otmar Scherzer, Nonstationary iterated Tikhonov-Morozov method and third order differential equations for the evaluation of unbounded operators, Mathematical Methods in the Applied Sciences 23(2000), 1287-1300.

C.W. Groetsch and M. Hanke, A general framework for regularized evaluation of unstable operators, Journal of Mathematical Analysis and Applications 203(1996), 451-463.

C.W. Groetsch, Inclusions and identities for the Moore-Penrose generalized inverse, Mathematische Nachrichten 171(1995), 157-164.

C.W. Groetsch and Otmar Scherzer, The optimal order of convergence for stable evaluation of differential operators, Electronic Journal of Differential Equations 4(1993), 1-12.

C.W. Groetsch, Inclusions for the Moore-Penrose inverse with applications to computational methods, in Contributions to Numerical Analysis (R.P. Agarwal, Ed.), World Scientific, Singapore, 1993, pp. 203-211.

C.W. Groetsch and A. Neubauer, Convergence of a general projection method for an operator equation of the first kind, Houston Journal of Mathematics 14(1988), 201-208.

G.D. Callon and C.W. Groetsch, The method of weighting and approximation of restricted pseudosolutions, Journal of Approximation Theory 5l (l987), ll-l8.

C.W. Groetsch, Generalized inverses and generalized splines, Numerical Functional Analysis and Optimization 2 (1980), 93-98.

C.W. Groetsch, Rates of convergence for approximations to the generalized inverse, Numerical Functional Analysis and Optimization 1(1979), 195-201.

C.W. Groetsch, A product integral representation of the generalized inverse, Commentationes Mathematicae Universitatis Carolinae 16, 1 (1975), 13-20.

C.W. Groetsch, Representations of the generalized inverse, Journal of Mathematical Analysis and Applications, 49 (1975) 154-157.

Applied Mathematics

D. A. French and C.W. Groetsch, Olfactory cilia: A case study in inverse modeling, pp. 1-12 in First Symposium on Inverse Problems and Applications, (J. Delgado et al., Eds.) , Universidad Autónoma Metropolitana, Ixtapa, Mexico, 2011, ISBN 978-607-477-505-1

C.W. Groetsch, Extending Halley’s Problem, The Mathematical Scientist 34(2009), 4-10.

C.W. Groetsch, A Torricellian model and implicit functions, The Mathematical Scientist 33(2008), 120-126.

D.A. French and C.W. Groetsch, Integral equation models for the inverse problem of biological ion channel distributions, Journal of Physics: Conference Series 73(2007) 102006, 10pp.

D.A. French, R. Flannery, C.W. Groetsch, S. Kleene and W. Krantz, Numerical approximation of solutions of a nonlinear inverse problem arising in olfaction experimentation, Mathematical and Computer Modelling 43(2006), 945-956.

C.W. Groetsch and Otmar Scherzer, Iterative stabilization and edge detection, in “Inverse Problems, Image Analysis, and Medical Imaging”, Contemporary Mathematics 313(2002), 129-142.

Otmar Scherzer and C.W. Groetsch, Inverse scale space theory for inverse problems, in Scale-Space and Morphology in Computer Vision (Michael Kerckhove, Ed.), Lecture Notes in Computer Science, Vol. 2106, pp. 317-325, Springer-Verlag, New York, 2001.

C.W. Groetsch, On the optimal angle of projection in general media, American Journal of Physics 65(1997), 797-799.

C.W. Groetsch and M. Hanke, Regularization of some one-dimensional inverse problems for identification of nonlinear surface phenomena, Proceedings of the 1995 Design Engineering Technical Conferences, Vol 3C, American Society of Mechanical Engineers, New York, pp. 903-908.

A. Binder, H.W. Engl, C.W. Groetsch, A. Neubauer and Otmar Scherzer, Weakly closed nonlinear operators and parameter identification in parabolic equations by Tikhonov regularization, Applicable Analysis 55(1995), 215-234.

Iterative Methods

C.W. Groetsch, The Forsythe-Motzkin method for singular linear operator equations, Journal of Optimization Theory and Applications 25 (1978), 311-315.

C.W. Groetsch and B. Jacobs, Iterative methods for generalized inverses based on functional interpolation, in "Recent Applications of Generalized Inverses" (Ed. S. Campbell), Pitman, London, 1982, pp. 220-232.

C.W. Groetsch, Relaxed steepest descent for singular linear operator equations, Rostocker Mathematisches Kolloquium 15 (1980), 45-54.

C.W. Groetsch, Some aspects of Mann's iterative method for approximating fixed points in "Fixed Points: Algorithms and Applications" (Ed. S. Karamardian), Academic Press, New York, 1977, pp. 349-365.

C.W. Groetsch, Ergodic theory and iterative solution of linear operator equations, Applicable Analysis, 5 (1976) 313-321.

C.W. Groetsch, Two remarks on the gradient method, Journal of Optimization Theory and Applications 17 (1975), 177-179.

C.W. Groetsch, Steepest descent and least squares solvability, Canadian Mathematics Bulletin, 17 (1974) 275-276.

C.W. Groetsch, A nonstationary iterative process for nonexpansive mappings, Proceedings of the American Mathematical Society, 43 (1974), 155-158.C.W. Groetsch, A note on segmenting Mann iterates, Journal of Mathematical Analysis and Applications, 40 (1972), 369-372.

Curtis Outlaw and C.W. Groetsch, Averaging iteration in a Banach space, Bulletin of the American Mathematical Society, 75 (1969), 430-432.

Classical Analysis

C.W. Groetsch, Lanczos' generalized derivative, The American Mathematical Monthly 105(1998), 320-326.

J. Bustoz and C.W. Groetsch, Approximation on the infinite interval by a class of positive linear operators, Mathematica 18 (1976), 26-33.

C.W. Groetsch and O. Shisha, On the degree of approximation by Bernstein polynomials, Journal of Approximation Theory 14(1975), 317-318.

J. Bustoz and C.W. Groetsch, Uniform approximation operators generated by a power series identity, SIAM Journal on Mathematical Analysis, 6 (1975), 472-479.

C. Groetsch, Summation methods associated with an iteration, Nanta Math. 7(1974), 13-16.

J. Bustoz and C.W. Groetsch, On generalized Bernstein polynomials, SIAM Journal on Mathematical Analysis, 5 (1974), 256-262.

C.W. Groetsch, Abel continuity of generalized Lototsky means, Rivista di Matematica (Parma), (3) 2(1973), 79-82.

C.W. Groetsch, Remarks on a generalization of the Lototsky summability method, Bolletino della Unione Matematica Italiana, 5 (1972), 277-288.

Mathematics for the College Classroom

C.W. Groetsch and A. Simoson, Spurtacular fountains, The Mathematical Gazette (London), to appear.

C.W. Groetsch, Galileo’s trajectory with mild resistance, International Journal of Mathematical Education in Science and Technology, to appear.

C.W. Groetsch, Spurt optimization, The Mathematical Gazette (London) 95(2011), 69-70.

C.W. Groetsch, Matter gravitates, but does gravity matter?, PRIMUS 21(2011), 142-148.

C.W. Groetsch, Suspension bridge profiles, The College Mathematics Journal 41(2010), 239-243.

C.W. Groetsch, The depletion ratio, The College Mathematics Journal 39(2008), 43-48.

C.W. Groetsch, From medieval scholasticism to cosmic exploration in three problems, PRIMUS 15(2005), 215-225.

C.W. Groetsch, Another broken symmetry, The College Mathematics Journal, 36(2005), 109-113.

C.W. Groetsch, Timing is everything: the French connection, The American Mathematical Monthly 110(2003), 950-955.

C.W. Groetsch, Geometrical aspects of an optimal trajectory, Pi Mu Epsilon Journal 11(2003), 1405-1408.

C.W. Groetsch, A celestial cubic, Mathematics Magazine 74(2001), 145-152.

C.W. Groetsch, Tartaglia’s bet, Cubo Matematica Educacional 6(2004), 15-21.

C.W. Groetsch, The commandant's corollary, The American Mathematical Monthly 107(2000), 15-23.

C.W. Groetsch, Aristotle's fall, The American Mathematical Monthly 105(1998), 544-547

C.W. Groetsch and Barry Cipra, Halley's comment - projectiles with linear resistance, Mathematics Magazine 70(1997), 273-280.

C.W. Groetsch, Equitemporal curves for resisted descent, Mathematics and Computer Education 31(1997), 152-157.

C.W. Groetsch, Halley's gunnery rule, The College Mathematics Journal 28(1997), 47-50.

C.W. Groetsch, Geophysically motivated inverse problems for the classroom, International Journal of Mathematical Education in Science and Technology 26(1995), 379-388.

C.W. Groetsch, Shapes of centroids as inverse problems, PRIMUS 3(1993), 315-322.

C.W. Groetsch, Inverse problems and Torricelli's law, The College Mathematics Journal 24(1993), 210-217.

C.W. Groetsch and B. Jacobs, Paper roll handling: A semigroup of affine transformations on Z^2 , International Journal of Mathematical Education in Science and Technology, 15(1984), 256-259.

G.B. Collins and C.W. Groetsch, An elementary mathematical problem arising in diatom taxonomy, International Journal of Mathematical Education in Science and Technology 12 (1980), 121-124.

C.W. Groetsch and J.T. King, The Bernstein polynomials and finite differences, Mathematics Magazine, 46 (1973), 280-282.

History of Mathematics; Biography

Kendall Atkinson and Charles Groetsch, M. Zuhair Nashed: A biographical tribute, Journal of Integral Equations and Applications 20(2008), 153-160.

C.W. Groetsch and M.Z. Nashed, Kendall Eugene Atkinson: an appreciation, Journal of Integral Equations and Applications 18(2006), 1-12.

C.W. Groetsch, Nascent function concepts in Nova Scientia, International Journal of Mathematical Education in Science and Technology 35(2004), 867-875.

C.W. Groetsch, The delayed emergence of regularization theory, Bollettino di Storia delle Scienze Matematiche, 23(2003), 105-120.

C.W. Groetsch, Hardy’s Duncan prize book, The Mathematical Intelligencer 25(2003) (No. 4), 5-6.

Charles Groetsch, E.W. Hyde 1843-1930, Mathematical Association of America – Ohio Section, 2001, http://sections.maa.org/ohio_masters/hyde.html

Charles Groetsch, Otto Szász 1884-1952, Mathematical Association of America – Ohio Section, 2001, http://sections.maa.org/ohio_masters/szasz.html

Charles Groetsch, Harris Hancock 1867-1944 Mathematical Association of America – Ohio Section, 2001 ,http://sections.maa.org/ohio_masters/hancock.html

Charles Groetsch, I.A. Barnett 1894-1974, Mathematical Association of America – Ohio Section, 2001, http://sections.maa.org/ohio_masters/barnett.html

Book Reviews

The Numerical Treatment of Integral Equations, by C.T.H. Baker, Oxford University Press, Oxford, 1977. Computing Reviews 19 (1978), 390.

The Numerical Solution of Volterra Equations, by Hermann Brunner and P.J. van der Houwen, North-Holland, Amsterdam, 1986. Mathematical Reviews 88g.65136.

Computational Methods for Integral Equations, by L.M. Delves and J.L. Mohamed, Cambridge University Press, Cambridge, 1985. SIAM Review 29(1987), 323-324.

Stable Solution of Inverse Problems, by Johann Baumeister, Vieweg, Braunschweig, 1987. Mathematical Reviews 89a65004.

Top-down Calculus, by S.G. Williamson, Computer Science Press, Rockville, MD, 1987. Computing Reviews 29(1988), 145-146.

Ill-posed Problems in the Natural Sciences, by A.N. Tikhonov and A.V. Goncharsky, MIR Publishers, Moscow, 1989. Mathematics of Computation 53(1989), 445-447.

Rank-deficient and Discrete Ill-posed Problems, by Per Christian Hansen, SIAM, Philadelphia, 1997. Zentralblatt für Mathematik 890.65037

An Introduction to the Mathematical Theory of Inverse Problems, by Andreas Kirsch, Springer-Verlag, New York, 1996. SIAM Review 39(1997), 794-796.

Regularization of Ill-posed Problems by Iteration Methods, by S.F. Gilyazov and N.N. Gol’dman, Kluwer, Dordrecht, 2000. Zentralblatt für Mathematik 943.65066

Operator Theory and Numerical Methods, by H. Fujita, N. Saito and T. Suzuki, Elsevier, Amsterdam, 2001. Mathematical Reviews 2002i65111

Introduction to the Mathematics of Medical Imaging, by Charles Epstein, Prentice-Hall, NJ, 2003. SIAM Review (2004), 14-16.

Charles Groetsch - Courses Taught

University of New Orleans (1966-68):Pre-calculus Mathematics I,IICollege AlgebraMath for Liberal Arts

Indiana University (1968-69):Calculus I,II

Louisiana State University (1969-71):Pre-calculus Mathematics I, IICalculus I,IIDifferential Equations

University of Rhode Island (1974-75):Calculus I,II

Theory of ProbabilityMathematical Logic

University of Cincinnati (1971-2006):Calculus I, II, III, IVFortran ProgrammingPL1 ProgrammingDifferential EquationsHonors Special TopicsOperations ResearchUndergraduate Numerical Analysis, I,IIGraduate Numerical Analysis I,II,IIIGraduate Seminar in Applied MathematicsGraduate Seminar in AnalysisMathematical ProgrammingProbability and StatisticsAdvanced Calculus I,IILinear AnalysisStatistics for Health SciencesFourier Series and Boundary Value ProblemsApplied Mathematics for EngineersAdvanced Applied Mathematics IIHistory of Mathematics I,IIIntroduction to Abstract MathematicsMathematics for the Social SciencesGeometry for High School TeachersLinear AlgebraLinear Algebra for HS TeachersMatrix MethodsGraduate AnalysisApplied Numerical AnalysisMathematical ModelsApplied Complex VariablesFunctional Analysis

The Citadel (2006 - ):Calculus I,IILinear AlgebraMathematical PhysicsMathematical Modeling (graduate)History of Mathematics (graduate)Introduction to AnalysisApplied Engineering Mathematics II

Short Courses :

Universität Kaiserslautern, Germany (1983):Graduate Seminar in Functional Analysis: Regularization Theory

Annual Meeting of the Mathematical Association of America (1992):Mini-course on Inverse Problems in the Undergraduate Classroom

Sixth Inverse Problems in Engineering Seminar (1994):Theoretical and Computational Aspects of Ill-posed Problems

Universidad Nacional de Colombia (1998)Inverse Problems and Theory of Operators

Hokkaido University, Japan (2006):Inverse Problems and Theory of Regularization

AIP12 Workshop, Texas A& M University, College Station (2011):Inverse Problems and Regularization Theory