Convergence analysis on a class of improved Chebyshev methods for nonlinear equations in Banach spaces

Xiuhua Wang and Jisheng Kou ()

Computational Optimization and Applications, 2015, vol. 60, issue 3, 697-717

Abstract: In this paper, we study the semilocal convergence on a class of improved Chebyshev methods for solving nonlinear equations in Banach spaces. Different from the results for Chebyshev method considered in Hernández and Salanova (J Comput Appl Math 126:131–143, 2000 ), these methods are free from the second derivative, the R-order of convergence is also improved. We prove a convergence theorem to show the existence-uniqueness of the solution. Under the convergence conditions used in Hernández and Salanova (J Comput Appl Math 126:131–143, 2000 ), the R-order for this class of methods is proved to be at least $$3+2p$$ 3 + 2 p , which is higher than the ones of Chebyshev method considered in Hernández and Salanova (J Comput Appl Math 126:131–143, 2000 ) and the variant of Chebyshev method considered in Hernández (J Optim Theory Appl 104(3): 501–515, 2000 ) under the same conditions. Copyright Springer Science+Business Media New York 2015

Keywords: Semilocal convergence; Recurrence relations; Nonlinear equations in Banach spaces; Hölder continuity; R-Order of convergence; 65D10; 65D99 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10589-014-9684-6

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