a neat idea, easy to do in Maxima, perhaps. Numerical derivatives
- Subject: a neat idea, easy to do in Maxima, perhaps. Numerical derivatives
- From: Richard Fateman
- Date: Fri, 04 Dec 2009 20:54:56 -0800
*Accurate numerical derivatives in MATLAB*
*Source*
ACM Transactions on Mathematical Software (TOMS) archive
<http://portal.acm.org/toc.cfm?id=J782&type=periodical&coll=portal&dl=ACM&CFID=525354554&CFTOKEN=525354554>;
Volume 33 , Issue 4 (August 2007) table of contents
<http://portal.acm.org/toc.cfm?id=1268776&type=issue&coll=portal&dl=ACM&CFID=525354554&CFTOKEN=525354554>;
Article No. 26
Year of Publication: 2007
ISSN:0098-3500
*Author *
L. F. Shampine
<http://portal.acm.org/author_page.cfm?id=81100197580&coll=portal&dl=ACM&trk=0&CFID=525354554&CFTOKEN=525354554>;
Southern Methodist University, Dallas, TX
*Publisher*
ACM <http://www.acm.org/publications>; New York, NY, USA
The basic observation is that if you can evaluate a function accurately
at a complex point, you have a way of getting very very accurate
numerical values of its derivative.
Observe that Im( f(x+i*h)) /h = f'(x)- h^3/6*f'''(x) + ....
solve for f'(x).
Much better than finite differences. Read the paper if you want more
interesting observations.
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