On the convergence of inexact quasi-newton methods

Abstract

This paper is concerned with quasi-Newton methods for solving systems of nonlinear equations, which make use of least-change secant updates. In the course of the iterative process, errors may be introduced and so the sequence actually computed differs from that produced in theory. Here, for this kind of perturbed procedures, usually called inexact quasi-Newton methods, a semilocal convergence analysis is carried out, giving a practical criterion for controlling the behaviour of the iterates. A continuation procedure is described, by which a “good” starting point, for the inexact quasi-Newton iteration, can be obtained. Furthermore, a posteriori error estimates are proposed and tested on numerical examples.