New improved convergence analysis for the secant method

Á. Alberto Magreñán and Ioannis K. Argyros

Mathematics and Computers in Simulation (MATCOM), 2016, vol. 119, issue C, 161-170

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. 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: 2016
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:119:y:2016:i:c:p:161-170

DOI: 10.1016/j.matcom.2015.08.002

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