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Re: minimax polynomial determination

• To: mathgroup at smc.vnet.net
• Subject: [mg115813] Re: minimax polynomial determination
• From: Ray Koopman <koopman at sfu.ca>
• Date: Fri, 21 Jan 2011 04:33:27 -0500 (EST)
• References: <ih3r5c$b8n$1@smc.vnet.net>

On Jan 18, 2:48 am, Leslaw Bieniasz <nbbie... at cyf-kr.edu.pl> wrote:
> Hi,
>
> 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.
>
> Leslaw

Use FindMinimum to find the locations of the zeros of f[x] - p[x].
Each function evaluation by FindMinimum requires multiple calls to
FindMaximum, one for each interval between the zeros of the error
curve; each such call returns the max abs error in that interval.
Remember that the endpoints of the overall interval will be either
zeros or extrema of the error curve.