nonLinearFit and nonLinearRegress

*To*: mathgroup at smc.vnet.net*Subject*: [mg55298] nonLinearFit and nonLinearRegress*From*: john.hawkin at gmail.com (John Hawkin)*Date*: Fri, 18 Mar 2005 05:34:55 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

I'm trying to do a nonLinear fit on some data, fitting a parameter which appears in the limits of the integral that I'm trying to fit. When I do a nonLinearFit, I get about a page of errors, but it does work. It takes about 10 minutes to do it for 20 points with a reasonable initial estimate. However when I use the nonLinearRegress command, even with the best fit parameter from nonLinearFit given as the initial guess, it takes hours to work. Is it possible there is a way to speed this up, and is this normal? The commands that I'm using to integrate this function are: h[B]:=2/(B pi) NIntegrate[x Sin[x] Exp[-(x/B)^3/2], {x, 0, inf}, Method-Oscillatory]; holts[c_, d_, Q_]:= NIntegrate[h[B], {B, c/Q, d/Q}]; where holts is the function I am fitting (the h[B] integral is known as the Holtsmark integral). The fitting command I'm using is: NonlinearFit[fitData, holts[c,d,Q], {c,d}, {Q, estimateQ}]; where fitData contains sets of size 3, with the values of c and d as the first two values, and the data point that I'm fitting the integral to as the 3rd value. If anyone has any ideas on how I can perform the nonlinear regression fast enough so that I can do it many times (maybe 50), I would greatly appreciate it. Thanks very much, John Hawkin

**Follow-Ups**:**Re: nonLinearFit and nonLinearRegress***From:*Daniel Lichtblau <danl@wolfram.com>

**Re: nonLinearFit and nonLinearRegress***From:*DrBob <drbob@bigfoot.com>