Re: Finding derivatives of a list?
- To: mathgroup at smc.vnet.net
- Subject: [mg40854] Re: [mg40816] Finding derivatives of a list?
- From: Daniel Lichtblau <danl at wolfram.com>
- Date: Tue, 22 Apr 2003 06:44:08 -0400 (EDT)
- References: <200304200302.XAA09952@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
AES/newspost wrote: > > Specific problem is how to generate a list of values of the second > derivative of a relatively smooth function at a set of equally spaced > points, when the function itself is known only as a list of numerical > values at those same points? > > -- > "Power tends to corrupt. Absolute power corrupts absolutely." > Lord Acton (1834-1902) > "Dependence on advertising tends to corrupt. Total dependence on > advertising corrupts totally." (today's equivalent) Here are some possibilities. (i) Form an interpolation of relatively high order (say 6 or so). Take second derivatives. (ii) Use finite differences to approximate the second derivatives. (iii) Use Fourier to get the approximated derivatives. See for example Wang, Jing. B (2002). Numerical differentiation using Fourier. The Mathematica Journal 8:3. 383-388. I believe there was a small error in the code provided; you might want to contact the author at wang at physics.uwa.edu.au Daniel Lichtblau Wolfram Research
- References:
- Finding derivatives of a list?
- From: AES/newspost <siegman@stanford.edu>
- Finding derivatives of a list?