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Re: minimax polynomial determination

• To: mathgroup at smc.vnet.net
• Subject: [mg115737] Re: minimax polynomial determination
• From: Bill Rowe <readnews at sbcglobal.net>
• Date: Wed, 19 Jan 2011 05:29:42 -0500 (EST)

On 1/18/11 at 5:48 AM, nbbienia at cyf-kr.edu.pl (Leslaw Bieniasz)
wrote:

>I need to determine minimax polynomial approximations to a certain
>function computed using MATHEMATICA. Unfortunately it is not
>possible to calculate exact derivatives of the function. Is there
>any way to use the MiniMaxApproximation[] algorithm with numerically
>approximated derivatives? I would appreciate an example.

A minmax approximation can be efficiently computed as a
Chebyshev series. You don't need to compute the derivative to
get the coefficients for a Chebyshev series. All you need do is
sample the function at appropriate points. Then the needed
coefficients can be computed using a discrete cosine transform.

See the applications section of ref/FourierDCT for details of
how to sample the function correctly and use FourierDCT to
compute the needed coefficients.