The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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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)
  • Received : 2010.09.22
  • Accepted : 2011.05.16
  • Published : 2011.05.31
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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.

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References

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