Generic Mathematica NonlinearRegress Question

*To*: mathgroup at smc.vnet.net*Subject*: [mg34715] Generic Mathematica NonlinearRegress Question*From*: qualsystems*nospam* at mindspring.com*Date*: Sun, 2 Jun 2002 01:14:53 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Hello, I am trying to find the best set of coefficients to a rather complicated function knowing only a few datapoints. I'm using NonlinearRegress for this with semi-acceptable results being returned from Mathematica. My queston is does anyone have any generic guidelines on the usage of MaxIterations, WorkingPrecision, AccuracyGoal, PrecisionGoal, Method , etc ? In other words, how can these and other inputs to NonlinearRegress be specified so as to exploit the search strategies being used by Mathematica. The documentation does not give a lot of info. to allow one to effectively set these. For example, when you have evidence that you have a set of coefficients that are near-optimal, say from a sum squared error basis, is it better to set MaxIterations to a high value (and risk an overflow or other error message) or set MaxIterations to a low value (and risk not searching the parameter-space thouroughly enough) ? How should these be set when you are just starting-out and therefore are most likely to be very far away from optimality ? Do these answers change if Newton as opposed to LevenbergMarquardt is being used ? I realize that the proper setting of starting values can dramatically affect the results, but there is much more to obtaining a good fit than specifying reasonable starting values. This is particularly the case when the phenomena being modeled has no underlying theoretical basis formula and therefore generic polynomials or other non-theoretic formulas need to be used. I also realize that fitting data to nonliear equations is equal parts computer science and art form and it is the art form that is compatible with a) how Mathematica searches for coefficients b) how Mathematica decides to stop searching and c) what Mathematica does in underflow, overflow, divide by zero and other circumstances that I am asking about. Is there a website or reference book that addresses these practical considerations ? Thanks. Steve