An inverse free broyden’s method for solving equations

Abstract

Based on a center-Lipschitz-type condition and our idea of the restricted convergence domain, we present a new semi-local convergence analysis for an inverse free Broyden’s method (BM) in order to approximate a locally unique solution of an equation in a Hilbert space setting. The operators involved have regularly continuous divided differences. This way we provide, weaker sufficient semi-local convergence conditions, tighter error bounds, and a more precise information on the location of the solution are provided in this study. Hence, our approach extends the applicability of BM under the same hypotheses as before. Finally, we consider some special cases. © 2020, International Publications. All rights reserved.