On finite termination of the generalized Newton method for solving absolute value equations

Jia Tang; Wenli Zheng; Cairong Chen; Dongmei Yu; Deren Han

doi:10.1007/s40314-023-02318-6

On finite termination of the generalized Newton method for solving absolute value equations

Jia Tang
, Wenli Zheng
, Cairong Chen^*
, Dongmei Yu
, Deren Han

^*Corresponding author for this work

School of Mathematical Sciences

Fujian Normal University
Liaoning Technical University

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

Motivated by the framework constructed by Brugnano and Casulli (SIAM J. Sci. Comput. 30: 463–472, 2008), we analyze the finite termination property of the generalized Netwon method (GNM) for solving the absolute value equation (AVE). More precisely, for some special matrices, GNM is terminated in at most 2 n+ 2 iterations. A new result for the unique solvability and unsolvability of the AVE is obtained. Numerical experiments are given to demonstrate the theoretical analysis.

Original language	English
Article number	187
Journal	Computational and Applied Mathematics
Volume	42
Issue number	4
DOIs	https://doi.org/10.1007/s40314-023-02318-6
State	Published - Jun 2023

Keywords

Absolute value equation
Finite termination
The generalized Newton method
Unique solvability
Unsolvability

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10.1007/s40314-023-02318-6

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title = "On finite termination of the generalized Newton method for solving absolute value equations",

abstract = "Motivated by the framework constructed by Brugnano and Casulli (SIAM J. Sci. Comput. 30: 463–472, 2008), we analyze the finite termination property of the generalized Netwon method (GNM) for solving the absolute value equation (AVE). More precisely, for some special matrices, GNM is terminated in at most 2 n+ 2 iterations. A new result for the unique solvability and unsolvability of the AVE is obtained. Numerical experiments are given to demonstrate the theoretical analysis.",

keywords = "Absolute value equation, Finite termination, The generalized Newton method, Unique solvability, Unsolvability",

author = "Jia Tang and Wenli Zheng and Cairong Chen and Dongmei Yu and Deren Han",

note = "Publisher Copyright: {\textcopyright} 2023, The Author(s) under exclusive licence to Sociedade Brasileira de Matem{\'a}tica Aplicada e Computacional.",

year = "2023",

month = jun,

doi = "10.1007/s40314-023-02318-6",

language = "英语",

volume = "42",

journal = "Computational and Applied Mathematics",

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TY - JOUR

T1 - On finite termination of the generalized Newton method for solving absolute value equations

AU - Tang, Jia

AU - Zheng, Wenli

AU - Chen, Cairong

AU - Yu, Dongmei

AU - Han, Deren

PY - 2023/6

Y1 - 2023/6

N2 - Motivated by the framework constructed by Brugnano and Casulli (SIAM J. Sci. Comput. 30: 463–472, 2008), we analyze the finite termination property of the generalized Netwon method (GNM) for solving the absolute value equation (AVE). More precisely, for some special matrices, GNM is terminated in at most 2 n+ 2 iterations. A new result for the unique solvability and unsolvability of the AVE is obtained. Numerical experiments are given to demonstrate the theoretical analysis.

AB - Motivated by the framework constructed by Brugnano and Casulli (SIAM J. Sci. Comput. 30: 463–472, 2008), we analyze the finite termination property of the generalized Netwon method (GNM) for solving the absolute value equation (AVE). More precisely, for some special matrices, GNM is terminated in at most 2 n+ 2 iterations. A new result for the unique solvability and unsolvability of the AVE is obtained. Numerical experiments are given to demonstrate the theoretical analysis.

KW - Absolute value equation

KW - Finite termination

KW - The generalized Newton method

KW - Unique solvability

KW - Unsolvability

UR - https://www.scopus.com/pages/publications/85160071612

U2 - 10.1007/s40314-023-02318-6

DO - 10.1007/s40314-023-02318-6

M3 - 文章

AN - SCOPUS:85160071612

SN - 2238-3603

VL - 42

JO - Computational and Applied Mathematics

JF - Computational and Applied Mathematics

IS - 4

M1 - 187

ER -

On finite termination of the generalized Newton method for solving absolute value equations

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Keywords

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