Minimum Residual BAS Iteration Method for Solving the System of Absolute Value Equations

被引：0

作者：

Dai, Yan-Xia ^{[1
]}

Yan, Ren-Yi ^{[2
]}

Yang, Ai-Li ^{[1
]}

机构：

[1] Hainan Normal Univ, Sch Math & Stat, Haikou 571158, Hainan, Peoples R China

[2] Hainan Normal Univ, Sch Econ & Management, Haikou 571158, Hainan, Peoples R China

来源：

COMMUNICATIONS ON APPLIED MATHEMATICS AND COMPUTATION | 2025年 / 7卷 / 05期

基金：

中国国家自然科学基金;

关键词：

Absolute value equations (AVEs); Block-diagonal and anti-block-diagonal splitting (BAS); Minimum residual; Minimum residual BAS (MRBAS) iteration; Convergence analysis; GENERALIZED NEWTON METHOD;

D O I：

10.1007/s42967-024-00403-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work, by applying the minimum residual technique to the block-diagonal and anti-block-diagonal splitting (BAS) iteration scheme, an iteration method named minimum residual BAS (MRBAS) is proposed to solve a two-by-two block system of nonlinear equations arising from the reformulation of the system of absolute value equations (AVEs). The theoretical analysis shows that the MRBAS iteration method is convergent under suitable conditions. Numerical results demonstrate the feasibility and the effectiveness of the MRBAS iteration method.

引用

页码：1815 / 1825

页数：11

共 39 条

[1]

[Anonymous], 1970, Classics in Applied Mathematics

[2]

Bai Z-Z., 2021, MATRIX ANAL COMPUTAT, DOI 10.1137/1.9781611976632

[3] Modulus-based synchronous multisplitting iteration methods for linear complementarity problems [J].

Bai, Zhong-Zhi ;

Zhang, Li-Li .

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 2013, 20 (03) :425-439

[4] Modulus-based matrix splitting iteration methods for linear complementarity problems [J].

Bai, Zhong-Zhi .

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 2010, 17 (06) :917-933

[5] Modified HSS iteration methods for a class of complex symmetric linear systems [J].

Bai, Zhong-Zhi ;

Benzi, Michele ;

Chen, Fang .

COMPUTING, 2010, 87 (3-4) :93-111

[6] On HSS-based iteration methods for weakly nonlinear systems [J].

Bai, Zhong-Zhi ;

Yang, Xi .

APPLIED NUMERICAL MATHEMATICS, 2009, 59 (12) :2923-2936

[7] Block and asynchronous two-stage methods for mildly nonlinear systems [J].

Bai, ZZ ;

Migallón, V ;

Penadés, J ;

Szyld, DB .

NUMERISCHE MATHEMATIK, 1999, 82 (01) :1-20

[8] Hermitian and skew-Hermitian splitting methods for non-hermitian positive definite linear systems [J].

Bai, ZZ ;

Golub, GH ;

Ng, MK .

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2003, 24 (03) :603-626

[9] A class of two-stage iterative methods for systems of weakly nonlinear equations [J].

Bai, ZZ .

NUMERICAL ALGORITHMS, 1997, 14 (04) :295-319

[10] Parallel multisplitting two-stage iterative methods for large sparse systems of weakly nonlinear equations [J].

Bai, ZZ .

NUMERICAL ALGORITHMS, 1997, 15 (3-4) :347-372

← 1 2 3 4 →