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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.18 No.2

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SEMILOCAL CONVERGENCE OF NEWTON’S METHOD FOR SINGULAR SYSTEMS WITH CONSTANT RANK DERIVATIVES

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2011, v.18 no.2, pp.97-111
https://doi.org/10.7468/jksmeb.2011.18.2.097
Argyros, Ioannis K.
Hilout, Said
Argyros,, I. K. , & Hilout,, S. (2011). SEMILOCAL CONVERGENCE OF NEWTON’S METHOD FOR SINGULAR SYSTEMS WITH CONSTANT RANK DERIVATIVES. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 18(2), 97-111, https://doi.org/10.7468/jksmeb.2011.18.2.097

Abstract

We provide a semilocal convergence result for approximating a solution of a singular system with constant rank derivatives, using Newton's method in an Euclidean space setting. Our approach uses more precise estimates and a combination of two Lipschitz-type conditions leading to the following advantages over earlier works [13], [16], [17], [29]: tighter bounds on the distances involved, and a more precise information on the location of the solution. Numerical examples are also provided in this study.

keywords
Newton's method, Euclidean space, singular system, constant rank derivative, Frechet derivative, Moore-Penrose matrix

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