New semilocal and local convergence analysis for the Secant method

Á. Alberto Magreñán and Ioannis K. Argyros

Applied Mathematics and Computation, 2015, vol. 262, issue C, 298-307

Abstract: We present a new convergence analysis, for the Secant method in order to approximate a locally unique solution of a nonlinear equation in a Banach space. Our idea uses Lipschitz and center-Lipschitz instead of just Lipschitz conditions in the convergence analysis. The new convergence analysis leads to more precise error bounds and to a better information on the location of the solution than the corresponding ones in earlier studies such as [2,6,9,11,14,15,17,20,22–26]. Numerical examples validating the theoretical results are also provided in this study.

Keywords: Secant method; Banach space; Majorizing sequence; Divided difference; Fréchet–derivative (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:262:y:2015:i:c:p:298-307

DOI: 10.1016/j.amc.2015.04.026

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