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