Semilocal Convergence of Steffensen-Type Algorithms for Solving Nonlinear Equations |
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Authors: | Hongmin Ren Ioannis K Argyros |
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Institution: | 1. College of Information and Engineering, Hangzhou Polytechnic , Zhejiang , P. R. China;2. Department of Mathematics Sciences , Cameron University , Lawton , Oklahoma , USA |
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Abstract: | In this article, we provide a semilocal analysis for the Steffensen-type method (STTM) for solving nonlinear equations in a Banach space setting using recurrence relations. Numerical examples to validate our main results are also provided in this study to show that STTM is faster than other methods (7 I. K. Argyros , J. Ezquerro , J. M. Gutiérrez , M. Hernández , and S. Hilout ( 2011 ). On the semilocal convergence of efficient Chebyshev-Secant-type methods . J. Comput. Appl. Math. 235 : 3195 – 3206 .Crossref], Web of Science ®] , Google Scholar], 13 J. A. Ezquerro and M. A. Hernández ( 2009 ). An optimization of Chebyshev's method . J. Complexity 25 : 343 – 361 .Crossref], Web of Science ®] , Google Scholar]]) using similar convergence conditions. |
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Keywords: | Banach space Derivative free method Divided difference Recurrence relations Semilocal convergence Steffensen-type method |
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