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
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.
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.
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