Re: ? numerical diff

From: Grave Digger <wizzerking@xxxxxxxxxxx>
Date: Mon, 14 Aug 2006 12:21:31 -0700

Cheng Cosine wrote:

Suppose we have a set of Chebyshev points fall in [-1, 1], and function

values at these points. We can use spectral numerical difference

to get high accuracy approximations for their derivatives at those points.

Porblem is, in real life, we cannot always take samples at Chebyshev nodes.

Often times, we have uniformly distributed sample points fall in whatever

interval. In this case, are there ways to use spectral numerical difference

or any other numerical difference methods to get high accuracy approx of

derivatives?

Thanks,
by Cheng Cosine
Aug/02/2k6 NC

Have you read about or Tried Savitzky-Golay ?
They pioneered a series of Least Squared polynomial smoothing functions which later were generalized and used as numerical differentiators.
The sole requirement for the Data was that the data be uniformly sampled, in you the space of you independant variable, usually time

A Google Search
http://www.google.com/search?hl=en&sa=X&oi=spell&resnum=0&ct=result&cd=1&q=savitzky+golay+differentiation&spell=1

may be useful
.

References:
- ? numerical diff
  - From: Cheng Cosine

Prev by Date: Stability of NR Gauss-Hermite algorithm in Excel/VBA?
Next by Date: Matlab fminunc just one iteration. Why?
Previous by thread: ? numerical diff
Next by thread: Re: ? numerical diff
Index(es):
- Date
- Thread

Relevant Pages

? numerical diff
... to get high accuracy approximations for their derivatives at those points. ... Porblem is, in real life, we cannot always take samples at Chebyshev nodes. ... are there ways to use spectral numerical difference ...
(sci.math.num-analysis)
Re: ? numerical diff
... are there ways to use spectral numerical difference ... accurate derivatives have existed from before the days of electronic ...
(sci.math.num-analysis)