Developing Secant Method for Solving Nonlinear Equations

Abstract

In this paper we develop secant methods for nonlinear system using a population of previous iterates. Contrarily to classic secant methods, where exact interpolation is used, we prefer a least square approach to calibrate the linear model. We address an explicit control of the numerical stability of the method. We show that our approach can lead to an update formula. In that case, we prove that the local convergence of the corresponding undamped quasi-Newton method.