Embed Size (px)
Transcript of Mescon logarithms
- 1. Base Agnostic Approximations of Logarithms
University of Evansville
Presented at MESCON 2011
Big Oh notation
Compares growth of functions
Common classes are
How does (log)fit?Compared to 1.5 or ()?
Topic barely addressed in texts
4. Approximation Technique 1
Integrate the log function
Note that log x is still present, presenting recursion
Did not pursue further
5. Approximation Technique 2
Derive the log function
What if we twiddle with the exponent by .01 and integrate?
6. Approximation 2 Results
Error at x = 50 is 4.2%
Error grows with increasing x
Can be reduced with more significant figures
7. Approximation Technique 3
Reasonable approximation truncates series
Argument must be < 1 to converge
8. Approximation 3 Results
Good approximation, even with only 3 terms
But approximation only valid for small region
9. Approximation Technique 4
Approximates minimax properties
Peak error is minimized in some interval
Slightly better convergence than Taylor
10. Approximation 4 Results
Centered about 0
Can be shifted
Really bad approximation outside region of convergence
Good approximation inside
Infinite series not well suited to task
Too much error in portions of number line
Derivation attempt is best
Suppose two algorithms run in (log)and (1.5)
Which is faster?
Since log=0.01, the(log) algorithm is faster.
13. What base is that?
Base in this presentation is always e.
Base conversion was insignificant portion of work
Change of Base formula always sufficient
14. The End
Slides will be posted on JoshWoody.com tonight
Questions, Concerns, or Comments?