On the Convergence of Broyden-Like Methods Using Recurrent Functions

In this article, we provide a finer semilocal convergence analysis of a certain class of Broyden-like methods for solving equations containing a nondifferentiable term on the p-dimensional Euclidean space (p ≥ 1, a natural number) [2 I.K. Argyros (2004). On the convergence of Broyden's method. Comm. Appl. Nonlinear Anal. 11:77–86. [Google Scholar], 4 I.K. Argyros ( 2007 ). Computational Theory of Iterative Methods, Series: Studies in Computational Mathematics, 15 ( C.K. Chui and L. Wuytack , eds.). Elsevier Publ. Co. , New York , USA . [Google Scholar], 5 I.K. Argyros ( 2007 ). On the convergence of Broyden–like methods . Acta Math. Sin. (Engl. Ser.) 23 : 2087 – 2096 .[Crossref] , [Google Scholar], 8 X. Chen ( 1990 ). On the convergence of Broyden–like methods for nonlinear equations with nondifferentiable terms . Ann. Inst. Statist. Math. 42 : 387 – 401 . [Google Scholar], 9 X. Chen and T. Yamamoto ( 1989 ). Convergence domains of certain iterative methods for solving nonlinear equations . Numer. Funct. Anal. Optim. 10 : 37 – 48 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]]. We achieve the goal by using our new idea of recurrent functions. Special cases and applications are also provided.