ON THE CONVERGENCE OF NEWTON'S METHOD ANDLOCALLY H？OLDERIAN OPERATORS

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081

2008, v.15 no.2, pp.111-120

Argyros, Ioannis K. (DEPARTMENT OF MATHEMATICAL SCIENCES, CAMERON UNIVERSITY)

Argyros, Ioannis K.. (2008). ON THE CONVERGENCE OF NEWTON'S METHOD AND LOCALLY <TEX>$H{\ddot{O}}LDERIAN$</TEX> OPERATORS. 한국수학교육학회지시리즈B:순수및응용수학, 15(2), 111-120.

복사

Abstract

A semi local convergence analysis is provided for Newton's method in a Banach space setting. The operators involved are only locally Holderian. We make use of a point-based approximation and center-Holderian hypotheses. This 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> operators, point-based approximation, semilocal convergence, successive substitutions, fixed point

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Vol.15 No.2

ON THE CONVERGENCE OF NEWTON'S METHOD AND LOCALLY <TEX>$H{\ddot{O}}LDERIAN$</TEX> OPERATORS

ON THE CONVERGENCE OF NEWTON'S METHOD ANDLOCALLY H？OLDERIAN OPERATORS

Abstract

한국수학교육학회지시리즈B:순수및응용수학