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MathGroup Archive 1996

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Re: Numerical Differentiation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg4296] Re: Numerical Differentiation
  • From: Mark Evans <evans at gte.net>
  • Date: Sat, 29 Jun 1996 03:56:26 -0400
  • Organization: GTE Intelligent Network Services, GTE INS
  • Sender: owner-wri-mathgroup at wolfram.com

Mark James wrote:
> 
> Does anyone know of a function that calculates the derivative of
> a function (that can't be differentiated symbolically) at a given
> point by numerical means?  I can't find it as a built-in or in the
> standard packages.  Thanks.

If you sample the function at even intervals, to obtain a "data stream," then 
you can get the first derivative with a simple digital filtering operation 
(discrete convolution using a special kernel).  It is also possible to get the 
second derivative, but I would not hold my hat for higher-order derivatives.

If this approach appeals to you, then let me know and I will send you my 
Mathematica work on the subject.  This work was done under contract with the 
specific objective of finding first- and second-order derivatives of a 
discrete data stream.

It turns out that the temporal spacing of the data samples (the sampling 
frequency) only contributes to the problem by introducing a scale factor.  You 
are free to select whatever sampling rate you like if you have an analytic 
function, but as with most other problems, the more points you include, the 
better the answer.

Mark Evans
evans at gte.net

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