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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Communicated by Ilio Galligani.
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Argyros, I.K., Hilout, S. Directional Secant-Type Methods for Solving Equations. J Optim Theory Appl 157, 462–485 (2013). https://doi.org/10.1007/s10957-012-0104-8
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DOI: https://doi.org/10.1007/s10957-012-0104-8