Iterative methods to solve the constrained Sylvester equation

被引：2

作者：

Yu, Siting ^{[1
]}

Peng, Jingjing ^{[1
]}

Tang, Zengao ^{[1
]}

Peng, Zhenyun ^{[1
]}

机构：

[1] Guilin Univ Elect Technol, Coll Math & Computat Sci, Guilin 541004, Peoples R China

来源：

AIMS MATHEMATICS | 2023年 / 8卷 / 09期

基金：

中国国家自然科学基金;

关键词：

nonlinear matrix equation; fixed point iteration algorithm; Anderson acceleration algorithm; Thompson distance; ALTERNATING PROJECTIONS; ANDERSON ACCELERATION; RICCATI EQUATION; MODEL-REDUCTION; MATRIX; ALGORITHM;

D O I：

10.3934/math.20231097

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the multiple constraint least squares solution of the Sylvester equation AX + XB = C is discussed. The necessary and sufficient conditions for the existence of solutions to the considered matrix equation are given. Noting that the alternating direction method of multipliers (ADMM) is a one-step iterative method, a multi-step alternating direction method of multipliers (MSADMM) to solve the considered matrix equation is proposed and some convergence results of the proposed algorithm are proved. Problems that should be studied in the near future are listed. Numerical comparisons between MSADMM, ADMM and ADMM with Anderson acceleration (ACADMM) are included.

引用

页码：21531 / 21553

页数：23

共 50 条

[41] Analysis of the solution of the Sylvester equation using low-rank ADI with exact shifts [J].

Truhar, Ninoslav ;

Tomljanovic, Zoran ;

Li, Ren-Cang .

SYSTEMS & CONTROL LETTERS, 2010, 59 (3-4) :248-257

[42] Noise-tolerant gradient-oriented neurodynamic model for solving the Sylvester equation [J].

Liu, Bei ;

Fu, Dongyang ;

Qi, Yimeng ;

Huang, Haoen ;

Jin, Long .

APPLIED SOFT COMPUTING, 2021, 109

[43] ON PMHSS ITERATION METHODS FOR CONTINUOUS SYLVESTER EQUATIONS [J].

Dong, Yongxin ;

Gu, Chuanqing .

JOURNAL OF COMPUTATIONAL MATHEMATICS, 2017, 35 (05) :600-619

[44] ON HERMITIAN AND SKEW-HERMITIAN SPLITTING ITERATION METHODS FOR CONTINUOUS SYLVESTER EQUATIONS [J].

Bai, Zhong-Zhi .

JOURNAL OF COMPUTATIONAL MATHEMATICS, 2011, 29 (02) :185-198

[45] A new procedure with iteration methods to solve a nonlinear two dimensional Bogoyavlensky-Konopelchenko equation [J].

Mohammed, Amal Jasim ;

Qasim, Ahmed Farooq .

JOURNAL OF INTERDISCIPLINARY MATHEMATICS, 2022, 25 (02) :537-552

[46] Unified Parametrization for the Solutions to the Polynomial Diophantine Matrix Equation and the Generalized Sylvester Matrix Equation [J].

Zhou, Bin ;

Yan, Zhi-Bin ;

Duan, Guang-Ren .

INTERNATIONAL JOURNAL OF CONTROL AUTOMATION AND SYSTEMS, 2010, 8 (01) :29-35

[47] Trapezoidal fully fuzzy Sylvester matrix equation with arbitrary coefficients [J].

Elsayed, Ahmed Abdelaziz ;

Ahmad, Nazihah ;

Malkawi, Ghassan .

SOFT COMPUTING, 2024, 28 (05) :4593-4606

[48] AN ERROR ANALYSIS FOR RATIONAL GALERKIN PROJECTION APPLIED TO THE SYLVESTER EQUATION [J].

Beckermann, Bernhard .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2011, 49 (06) :2430-2450

[49] Some iterative methods for the largest positive definite solution to a class of nonlinear matrix equation [J].

Bao-Hua Huang ;

Chang-Feng Ma .

Numerical Algorithms, 2018, 79 :153-178

[50] Some iterative methods for the largest positive definite solution to a class of nonlinear matrix equation [J].

Huang, Bao-Hua ;

Ma, Chang-Feng .

NUMERICAL ALGORITHMS, 2018, 79 (01) :153-178

← 1 2 3 4 5 →