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
收藏
页码：21531 / 21553
页数：23
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