Semi local convergence of secant-like methods for differentiable and nondifferentiable operator equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:398

Article

Ezquerro, J. A.¹  Grau-Sanchez, M.²  Hernandez, M. A.¹  Noguera, M.² 

[1] Univ La Rioja, Dept Math & Computat, Logrono 26004, Spain

[2] Tech Univ Catalonia, Dept Appl Math 2, Barcelona 08034, Spain

关键词: Nonlinear equations;    Divided difference;    Iterative method;    The secant method;    Kurchatov's method;    Order of convergence;    Computational efficiency;    Conservative problem;   

DOI  :  10.1016/j.jmaa.2012.08.040

来源: Elsevier

【 摘 要 】

From well-known secant-like methods, we observe that we can construct a new family of secant-like methods that includes the secant method and Kurchatov's method. We analyse the local orders of convergence and the efficiencies of the methods of the family and study the semilocal convergence for differentiable and nondifferentiable operators. Finally, we apply our results to conservative problems. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free