On the convergence of Broyden's method with regularity continuous divided differences and restricted convergence domains

Abstract

We present a semilocal convergence analysis for Broyden's method with regularly continuous divided differences in a Banach/Hilbert space setting. By using: center-Lipschitz-type conditions defining restricted convergence domains, at least as weak hypotheses and the same computational cost as in [6] we provide a new convergence analysis for Broyden's method with the following advantages: larger convergence domain; finer error bounds on the distances involved, and at least as precise information on the location of the solution. © 2017 Journal of Nonlinear Functional Analysis.