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

Said Hilout|Ioannis K. Argyros
한국수학교육학회|2011.05|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제18권 제2호|pp. 97-111

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참고문헌

키워드

Newton’s methodEuclidean spacesingular systemconstant rank de-rivativeFréchet derivativeMoore–Penrose matrix.
주제분류수학

초록

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 combi-nation 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.

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 combi-nation 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.

참고문헌 (29)

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관련 논문AI추천

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