A relaxed generalized Newton iteration method for generalized absolute value equations

To avoid singular generalized Jacobian matrix and further accelerate the convergence of the generalized Newton (GN) iteration method for solving generalized absolute value equations Ax - B|x| = b, in this paper we propose a new relaxed generalized Newton (RGN) iteration method by introducing a relax...

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Published inAIMS mathematics Vol. 6; no. 2; pp. 1258 - 1275
Main Authors Cao, Yang, Shi, Quan, Zhu, Sen-Lai
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2021
Subjects
generalized absolute value equations
globally convergence
newton method
relaxation
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ISSN2473-6988
2473-6988
DOI10.3934/math.2021078

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Abstract To avoid singular generalized Jacobian matrix and further accelerate the convergence of the generalized Newton (GN) iteration method for solving generalized absolute value equations Ax - B|x| = b, in this paper we propose a new relaxed generalized Newton (RGN) iteration method by introducing a relaxation iteration parameter. The new RGN iteration method involves the well-known GN iteration method and the Picard iteration method as special cases. Theoretical analyses show that the RGN iteration method is well defined and globally linearly convergent under suitable conditions. In addition, a specific sufficient condition is studied when the coefficient matrix A is symmetric positive definite. Finally, two numerical experiments arising from the linear complementarity problems are used to illustrate the effectiveness of the new RGN iteration method.
AbstractList To avoid singular generalized Jacobian matrix and further accelerate the convergence of the generalized Newton (GN) iteration method for solving generalized absolute value equations Ax - B|x| = b, in this paper we propose a new relaxed generalized Newton (RGN) iteration method by introducing a relaxation iteration parameter. The new RGN iteration method involves the well-known GN iteration method and the Picard iteration method as special cases. Theoretical analyses show that the RGN iteration method is well defined and globally linearly convergent under suitable conditions. In addition, a specific sufficient condition is studied when the coefficient matrix A is symmetric positive definite. Finally, two numerical experiments arising from the linear complementarity problems are used to illustrate the effectiveness of the new RGN iteration method.
Author Zhu, Sen-Lai
Cao, Yang
Shi, Quan
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CorporateAuthor School of Transportation and Civil Engineering, Nantong University, Nantong, 226019, P. R. China
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StartPage 1258
SubjectTerms generalized absolute value equations
globally convergence
newton method
relaxation
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Title A relaxed generalized Newton iteration method for generalized absolute value equations
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