Re: Bug in MiniMaxApproximation
- To: mathgroup at smc.vnet.net
- Subject: [mg60649] Re: Bug in MiniMaxApproximation
- From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
- Date: Fri, 23 Sep 2005 04:19:53 -0400 (EDT)
- Organization: The Open University, Milton Keynes, U.K.
- References: <dgtisl$25n$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
dh wrote:
> 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
>
Daniel,
Since "[...] minimax approximation r(x) to a given function f(x) is the
rational function of the given degree that minimizes the maximum value
of the quantity | 1 - r(x) / f(x) | over the interval under
consideration," it is no wonder that when f(0) == 0 you get a division
by wero error.
Check the paragraph after the graphics "Out[7]":
http://documents.wolfram.com/mathematica/Add-onsLinks/StandardPackages/NumericalMath/Approximations.html
Regards,
/J.M.