Re: minimax polynomial determination

*To*: mathgroup at smc.vnet.net*Subject*: [mg115819] Re: minimax polynomial determination*From*: Ray Koopman <koopman at sfu.ca>*Date*: Fri, 21 Jan 2011 04:34:37 -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 Further to my first post, I seem to remember that, when I've done this sort of thing in the past, I've had better luck with FindRoot than with FindMinimum as the outer function. Instead of minimizing the max of the absolute values of the local extrema of the error curve, set the sums of adjacent pairs of signed local extrema all to zero. The inner calls would be to a "findExtremum", which would return a local min or max.