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.