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Semilocal Convergence Theorem for a Newton-like Method

Part of: Numerical linear algebra Nonlinear algebraic or transcendental equations

Published online by Cambridge University Press:  07 September 2017

Rong-Fei Lin ,
Qing-Biao Wu ,
Min-Hong Chen ,
Lu Liu  and
Ping-Fei Dai
Rong-Fei Lin*
Affiliation:
Department of Mathematics, Taizhou University, Linhai 317000, Zhejiang, China
Qing-Biao Wu*
Affiliation:
Department of Mathematics, Zhejiang University, Hangzhou 310027, Zhejiang, China
Min-Hong Chen*
Affiliation:
Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou 310012, Zhejiang, China
Lu Liu*
Affiliation:
Department of Mathematics, Zhejiang University, Hangzhou 310027, Zhejiang, China
Ping-Fei Dai*
Affiliation:
Department of Mathematics, Zhejiang University, Hangzhou 310027, Zhejiang, China
*
*Corresponding author. Email addresses:[email protected] (R.-F. Lin), [email protected] (Q.-B. Wu), [email protected] (M.-H. Chen), [email protected] (L. Liu), [email protected] (P.-F. Dai)
*Corresponding author. Email addresses:[email protected] (R.-F. Lin), [email protected] (Q.-B. Wu), [email protected] (M.-H. Chen), [email protected] (L. Liu), [email protected] (P.-F. Dai)
*Corresponding author. Email addresses:[email protected] (R.-F. Lin), [email protected] (Q.-B. Wu), [email protected] (M.-H. Chen), [email protected] (L. Liu), [email protected] (P.-F. Dai)
*Corresponding author. Email addresses:[email protected] (R.-F. Lin), [email protected] (Q.-B. Wu), [email protected] (M.-H. Chen), [email protected] (L. Liu), [email protected] (P.-F. Dai)
*Corresponding author. Email addresses:[email protected] (R.-F. Lin), [email protected] (Q.-B. Wu), [email protected] (M.-H. Chen), [email protected] (L. Liu), [email protected] (P.-F. Dai)
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Abstract

The semilocal convergence of a third-order Newton-like method for solving nonlinear equations is considered. Under a weak condition (the so-called γ-condition) on the derivative of the nonlinear operator, we establish a new semilocal convergence theorem for the Newton-like method and also provide an error estimate. Some numerical examples show the applicability and efficiency of our result, in comparison to other semilocal convergence theorems.

Keywords

Newton-like methodnonlinear equationNewton-Kantorovich theoremγ-conditionerror estimate

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 3 , August 2017 , pp. 482 - 494
Copyright
Copyright © Global-Science Press 2017 

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