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MathGroup Archive 2005

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Re: Bug in MiniMaxApproximation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg60664] Re: Bug in MiniMaxApproximation
  • From: Peter Pein <petsie at dordos.net>
  • Date: Fri, 23 Sep 2005 04:20:16 -0400 (EDT)
  • References: <dgtisl$25n$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

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)
-- 
Peter Pein, Berlin
GnuPG Key ID: 0xA34C5A82
http://people.freenet.de/Peter_Berlin/


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