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Generic Mathematica NonlinearRegress Question

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


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 ?



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