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http://dx.doi.org/10.7468/jksmeb.2011.18.2.097

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

Argyros, Ioannis K. (Cameron University, Department of Mathematics Sciences)
Hilout, Said (Poitiers University, Laboratoire de Mathmematiques et Applications)
Publication Information
The Pure and Applied Mathematics / v.18, no.2, 2011 , pp. 97-111 More about this Journal
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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