Semilocal Convergence of a Class of Modified Super-Halley Methods in Banach Spaces

Xiuhua Wang, Jisheng Kou () and Chuanqing Gu
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Xiuhua Wang: Xiaogan University
Jisheng Kou: Xiaogan University
Chuanqing Gu: Shanghai University

Journal of Optimization Theory and Applications, 2012, vol. 153, issue 3, No 14, 779-793

Abstract: Abstract In this paper, we consider the semilocal convergence of a class of modified super-Halley methods for solving nonlinear equations in Banach spaces. The semilocal convergence of this class of methods is established by using recurrence relations. We construct a system of recurrence relations for the methods, and based on it, we prove an existence–uniqueness theorem that shows the R-order of the methods.

Keywords: Nonlinear equations in Banach spaces; Semilocal convergence; Recurrence relations; Super-Halley method; Iterative method (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-012-9985-9

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