A global strategy for nonlinear least squares

Abstract

A general strategy for attacking problems in nonlinear least squares is developed. Parameters are classified as linear or nonlinear, depending on whether they appear linearly or nonlinearly in the functional expression being fitted to a set of data.Basically the strategy consists of transforming the functional expression so as to maximize the number of linear parameters and then solving the problem in a two-stage process. For given values of the nonlinear parameters the linear parameters are first defined as functions of the nonlinear parameters by the solution of a linear regression. The nonlinear parameters are then found by minimizing the usual quadratic form with the use of standard search techniques.