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2012 Semilocal Convergence Analysis for Inexact Newton Method under Weak Condition
Xiubin Xu, Yuan Xiao, Tao Liu
Abstr. Appl. Anal. 2012: 1-13 (2012). DOI: 10.1155/2012/982925

Abstract

Under the hypothesis that the first derivative satisfies some kind of weak Lipschitz conditions, a new semilocal convergence theorem for inexact Newton method is presented. Unified convergence criteria ensuring the convergence of inexact Newton method are also established. Applications to some special cases such as the Kantorovich type conditions and γ -Conditions are provided and some well-known convergence theorems for Newton's method are obtained as corollaries.

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Xiubin Xu. Yuan Xiao. Tao Liu. "Semilocal Convergence Analysis for Inexact Newton Method under Weak Condition." Abstr. Appl. Anal. 2012 1 - 13, 2012. https://doi.org/10.1155/2012/982925

Information

Published: 2012
First available in Project Euclid: 28 March 2013

zbMATH: 1246.90146
MathSciNet: MR2965468
Digital Object Identifier: 10.1155/2012/982925

Rights: Copyright © 2012 Hindawi

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