A Rapidly Convergent Iterative Method for the Solution of the Generalised Nonlinear Least Squares Problem

Abstract

A new iterative method is described for the solution of the generalised nonlinear least squares problem: where the model may be nonlinear in its parameters and in the independent variable(s) and all variables are subject to error. The method is described for the case of two arbitrarily related variables; does not require the analytic calculation of derivatives; leads to exceptionally close satisfaction of the least squares conditions; and exhibits especially rapid convergence arising from the use of somewhat unconventional numerical approximations for partial derivatives. Examples are given which compare the results of the method of those of other existing techniques.