Expanding the applicability of the Secant method under weaker conditions

Ioannis K. Argyros and Á. Alberto Magreñán

Applied Mathematics and Computation, 2015, vol. 266, issue C, 1000-1012

Abstract: We present a new semilocal convergence analysis for Secant method in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Our analysis includes the computation of the bounds on the limit points of the majorizing sequences involved. Under the same computational cost on the parameters involved our convergence criteria are weaker and the error bounds more precise than in earlier studies such as (Amat and Busquier, 2003; Amat et al., in press; Argyros and Hilout, 2012; Argyros et al., 2014; Argyros and Magreñán, 2014, 2015; Dennis, 1971; Ezquerro et al., 2000; Ortega and Rheinboldt, 1970; Potra and Pták, 1984; Schmidt, 1978). Numerical examples are also presented to illustrate the theoretical results obtained in this study.

Keywords: Secant method; Banach space; Majorizing sequence; Divided difference; Local convergence; Semilocal convergence (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:266:y:2015:i:c:p:1000-1012

DOI: 10.1016/j.amc.2015.06.037

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