Semilocal convergence analysis on the modifications for Chebyshev–Halley methods under generalized condition

Xiuhua Wang and Jisheng Kou

Applied Mathematics and Computation, 2016, vol. 281, issue C, 243-251

Abstract: In this paper, we consider the semilocal convergence for modifications of Chebyshev–Halley methods in Banach space. Compared with the results on super-Halley method studied in reference Gutiérrez and Hernández (1998)these modified methods need less computation of inversion, the R-order is improved, and the Lipschitz continuity of second derivative is also relaxed. We prove a theorem to show existence-uniqueness of solution. The R-order for these modified methods is analyzed under generalized condition.

Keywords: Semilocal convergence; Nonlinear equation in Banach space; Lipschitz continuity; Chebyshev–Halley methods; Generalized condition (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:281:y:2016:i:c:p:243-251

DOI: 10.1016/j.amc.2016.01.035

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