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Semilocal Convergence Analysis for MMN-HSS Methods under Hölder Conditions

Part of: Numerical linear algebra Nonlinear algebraic or transcendental equations

Published online by Cambridge University Press:  02 May 2017

Yang Li  and
Xue-Ping Guo
Yang Li*
Affiliation:
Department of Mathematics, East China Normal University, Shanghai 200241, China
Xue-Ping Guo*
Affiliation:
Department of Mathematics, East China Normal University, Shanghai 200241, China
*
*Corresponding author. Email addresses:jlqaplum@163.com (Y. Li), xpguo@math.ecnu.edu.cn (X.-P. Guo)
*Corresponding author. Email addresses:jlqaplum@163.com (Y. Li), xpguo@math.ecnu.edu.cn (X.-P. Guo)
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Abstract

Multi-step modified Newton-HSS (MMN-HSS) methods, which are variants of inexact Newton methods, have been shown to be competitive for solving large sparse systems of nonlinear equations with positive definite Jacobian matrices. Previously, we established these MMN-HSS methods under Lipschitz conditions, and we now present a semilocal convergence theorem assuming the nonlinear operator satisfies milder Hölder continuity conditions. Some numerical examples demonstrate our theoretical analysis.

Keywords

MMN-HSS methodlarge sparse systems of nonlinear equationHölder conditionspositive-definite Jacobian matricessemilocal convergence

MSC classification

Secondary: 65F10: Iterative methods for linear systems 65F50: Sparse matrices 65H10: Systems of equations
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 7 , Issue 2 , May 2017 , pp. 396 - 416
Copyright
Copyright © Global-Science Press 2017 

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