Re: minimax polynomial determination

*To*: mathgroup at smc.vnet.net*Subject*: [mg115813] Re: minimax polynomial determination*From*: Ray Koopman <koopman at sfu.ca>*Date*: Fri, 21 Jan 2011 04:33:27 -0500 (EST)*References*: <ih3r5c$b8n$1@smc.vnet.net>

On Jan 18, 2:48 am, Leslaw Bieniasz <nbbie... at cyf-kr.edu.pl> wrote: > Hi, > > I need to determine minimax polynomial approximations to a certain > function computed using MATHEMATICA. Unfortunately it is not possible > to calculate exact derivatives of the function. Is there any way to use > the MiniMaxApproximation[] algorithm with numerically approximated > derivatives? I would appreciate an example. > > Leslaw Use FindMinimum to find the locations of the zeros of f[x] - p[x]. Each function evaluation by FindMinimum requires multiple calls to FindMaximum, one for each interval between the zeros of the error curve; each such call returns the max abs error in that interval. Remember that the endpoints of the overall interval will be either zeros or extrema of the error curve.