Interpolation problem, optimization algorithms

*To*: mathgroup at smc.vnet.net*Subject*: [mg58916] Interpolation problem, optimization algorithms*From*: Ed Peschko <esp5 at mdssdev05.comp.pge.com>*Date*: Sat, 23 Jul 2005 05:32:43 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

hey all, I have a group of very noisy functions that I want to interpolate and simplify and they have two things in common: they are diophantine, positive, and are almost linear over certain ranges. For example, one function might be linear for the first 10 values of x, then have a different linear approximation over 11-50, then a different one over 51-100, etc. Hence, I'd like to simplify them into piecewise linear functions, ie: f[x_] := a1 * x + b1 /; x < 10; f[x_] := a2 * x + b2 /; 10 <= x < 50; f[x_] := a3 * x + b3 /; 50 <= x < 100; f[x_] := b4 /; x >= 100; The main thing is, however, that I don't know beforehand *which* ranges correspond to which equations - its not all that clear by just looking at the graphs - and I'd like to find the best fit possible for each. Anyways, what I was wondering was - how do the Interpolation and ListInterpolation functions work? Can you make them non-black box, and put constraints on them like those listed above? And if not, what approach would people suggest that I take? I've already tried NMinimize with pretty poor results; the functions are slow, and don't seem to converge to good solutions. Ed ( ps - is there a 'beefed up' version of the algorithms to do minimization problems inside of Mathematica? The one thing that I *did* try which seemed to have good results was to hand-code a c program to do fitting and feed it into a package called adaptive simulated annealing.. But even then I'm not guaranteed an optimum fit, the times to find it are slow, and I'd rather have a mathematica-only solution if possible. )