Directional Secant‐Type Methods for Solving Equations

Directional Secant‐Type Methods for Solving Equations

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Article ID: iaor20132830
Volume: 157
Issue: 2
Start Page Number: 462
End Page Number: 485
Publication Date: May 2013
Journal: Journal of Optimization Theory and Applications
Authors: ,
Keywords: heuristics
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.

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