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.