A note on solving nonlinear equations and the natural criterion function

Abstract

We consider the natural criterion function for controlling a damped Newton iteration used for solving systems of nonlinear equations. An example is given which shows that the method can cycle in an undesirable manner, not possible when using the more conventional least-squares criterion function. Despite this, the natural criterion function is of value in particular applications. This point is illustrated using a system derived from a nonlinear two-point boundary-value problem.