A Kantorovich-type analysis for a fast iterative method for solving nonlinear equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:332

Article

Argyros, Ioannis K.

关键词: Banach space;    majorant principle;    secant method;    locallsemilocal convergence;    radius of convergence;    Lipschitz conditions;    divided differences;   

DOI  :  10.1016/j.jmaa.2006.09.075

来源: Elsevier

【 摘 要 】

We revisit a fast iterative method studied by us in [I.K. Argyros, On a two-point Newton-like method of convergent order two, Int. J. Comput. Math. 88 (2) (2005) 219-234] to approximate solutions of nonlinear operator equations. The method uses only divided differences of order one and two function evaluations per step. This time we use a simpler Kantorovich-type analysis to establish the quadratic convergence of the method in the local as well as the semilocal case. Moreover we show that in some cases our method compares favorably, and can be used in cases where other methods using similar information cannot [S. Amat, S. Busquier, V.F. Candela, A class of quasi-Newton generalized Steffensen's methods on Banach spaces, J. Comput. Appl. Math. 149 (2) (2002) 397-406; D. Chen, On the convergence of a class of generalized Steffensen's iterative procedures and error analysis, Int. J. Comput. Math. 31 (1989) 195-203]. Numerical examples are provided to justify the theoretical results. (c) 2006 Elsevier Inc. All rights reserved.

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