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)