Re: Bug in MiniMaxApproximation
- To: mathgroup at smc.vnet.net
- Subject: [mg60675] Re: Bug in MiniMaxApproximation
- From: dh <dh at metrohm.ch>
- Date: Sat, 24 Sep 2005 02:55:21 -0400 (EDT)
- References: <dgtisl$25n$1@smc.vnet.net> <dh0f7t$qcn$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Hallo Peter, vielen Dank für Deine Antwort. Weisst Du vielleicht ob es irgendwo eine allgemeine MiniMax Mathematica Routine gibt. z.B. eine Mathematica Implementation des Remez or Parks-McClellan algorithmus. Gruss, Daniel Moderator's rough translation - Hello Peter - Thank you for your answer. Perhaps you know whether there is a general MiniMax Mathematica routine e.g. a Mathematica implementation of the Remez or Parks-McClellen alogrithms. Thank you, Daniel Peter Pein wrote: > dh schrieb: > >>Hello, >>it seems to me that MiniMaxApproximation fails each time the given >>function is zero at the beginning of the specified interval >>Consider an example from the Help: >> >>MiniMaxApproximation[Exp[x],{x, {0, 2}, 2, 4}] >> >>this works fine. However, if you change the function to 1-Exp[..]: >> >>MiniMaxApproximation[1 - Exp[x], {x, {0, 2}, 2, 4}] >> >>you get an 1/0 error. >> >>sincerely, Daniel >> > > Hi Daniel, > > from the docs: > "Because MiniMaxApproximation tries to minimize the maximum of the > relative error, it is not possible to find a minimax approximation to a > function that has a zero in the interval in question. " > > > mm = x*MiniMaxApproximation[Piecewise[{{-1, x == 0}}, (1 - Exp[x])/x], > {x, {0, 2}, 1, 4}][[2,1]] > > ((-1.0000021205528822 - 0.204709852011999*x)*x)/ > (1 - 0.2952222393355634*x - 0.01939552534357132*x^2 + > 0.017813878338228693*x^3 - 0.0020804136873956523*x^4)