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Re: MiniMaxApproximation question

• To: mathgroup at smc.vnet.net
• Subject: [mg61946] Re: [mg61908] MiniMaxApproximation question
• From: "Jose Luis Gomez" <jose.luis.gomez at itesm.mx>
• Date: Sat, 5 Nov 2005 01:52:49 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

Michael
I am not sure, but I think that the standard AddOn <<Calculus`Pade` might be
useful for you. See this link:

http://documents.wolfram.com/mathematica/Add-onsLinks/StandardPackages/Calcu
lus/Pade.html 

Hope that helps 
Jose

-----Mensaje original-----
De: michael_chang86 at hotmail.com [mailto:michael_chang86 at hotmail.com] 
Enviado el: Viernes, 04 de Noviembre de 2005 04:11 a.m.
Para: mathgroup at smc.vnet.net
Asunto: [mg61908] MiniMaxApproximation question

Hi,

I'm using Mathematica 5.2, and was wondering if one easily can obtain a
rational (preferably with degree(denominator)=0) mini-max polynomial
approximation of a function f[x] (à la MiniMaxApproximation), where
the *absolute* error is minimized over a finite region.  A quick
perusal of the documentation for MiniMaxApproximation indicates that
the *relative* error is optimized.

Specifically, I would like to obtain an optimal (with regards to the
*absolute* error) approximation  of:

x^d, x \in [0,1], 0<d<\infty.

One can, of course, obtain a simple polynomial approximation using
Chebyshev's discrete interpolation formula (after a simple
translation), but I was wondering if one can easily improve the
(absolute error) approximation via MiniMaxApproximation (or some other
unknown variant thereof).

Many thanks in advance!

Michael