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MiniMaxApproximation question

• To: mathgroup at smc.vnet.net
• Subject: [mg61908] MiniMaxApproximation question
• From: michael_chang86 at hotmail.com
• Date: Fri, 4 Nov 2005 05:11:29 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

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