ON THE CONVERGENCE OF NEWTON'S METHOD AND LOCALLY HÖLDERIAN INVERSES OF OPERATORS

Argyros, Ioannis K.; Argyros, Ioannis K.

P-ISSN1226-0657
E-ISSN2287-6081
KCI

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Vol.16 No.1

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ON THE CONVERGENCE OF NEWTON'S METHOD AND LOCALLY HÖLDERIAN INVERSES OF OPERATORS

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

2009, v.16 no.1, pp.13-18

Argyros, Ioannis K.

Argyros,, I. K. (2009). ON THE CONVERGENCE OF NEWTON'S METHOD AND LOCALLY HÖLDERIAN INVERSES OF OPERATORS. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 16(1), 13-18.

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Abstract

A semilocal convergence analysis is provided for Newton's method in a Banach space. The inverses of the operators involved are only locally <TEX>$H{\ddot{o}}lderian$</TEX>. We make use of a point-based approximation and center-<TEX>$H{\ddot{o}}lderian$</TEX> hypotheses for the inverses of the operators involved. Such an approach can be used to approximate solutions of equations involving nonsmooth operators.

keywords: Newton's method, Banach space, locally <tex> $H{\ddot{o}}lderian$</tex> inverses of operators, point-based approximation, semilocal convergence, successive substitutions, fixed point

Reference

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Article Contents

Vol.16 No.1

ON THE CONVERGENCE OF NEWTON'S METHOD AND LOCALLY HÖLDERIAN INVERSES OF OPERATORS

Abstract

Reference

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics