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

Argyros, I.K.George, S.2020-03-312020-03-312017Journal of Nonlinear Functional Analysis, 2017, Vol.2017, , pp.-https://idr.nitk.ac.in/handle/123456789/12373We 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.On the convergence of Broyden's method with regularity continuous divided differences and restricted convergence domainsArticle