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