A theory of secant preconditioners

Abstract

In this paper we analyze the use of structured quasi-Newton formulae as preconditioners of iterative linear methods when the inexact-Newton approach is employed for solving nonlinear systems of equations. We prove that superlinear convergence and bounded work per iteration is obtained if the preconditioners satisfy a Dennis-Moré condition. We develop a theory of Least-Change Secant Update preconditioners and we present an application concerning a structured BFGS preconditioner.