Directional Secant-Type Methods for Solving Equations

Ioannis K. Argyros () and Saïd Hilout ()
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Ioannis K. Argyros: Cameron University
Saïd Hilout: Poitiers University

Journal of Optimization Theory and Applications, 2013, vol. 157, issue 2, No 9, 462-485

Abstract: Abstract A semilocal convergence analysis for directional Secant-type methods in multidimensional space is provided. Using weaker hypotheses than the ones exploited by An and Bai, we provide a semilocal convergence analysis with the following advantages: weaker convergence conditions, larger convergence domain, finer error estimates on the distances involved, and more precise information on the location of the solution. A numerical example, where our results apply to solve an equation but not the ones of An and Bai, is also provided. In a second example, we show how to implement the method.

Keywords: Directional Secant-type method; Directional Newton method; Nonlinear equations; Newton–Kantorovich hypotheses; Lipschitz/center-Lipschitz condition (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10957-012-0104-8

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