Gradient-Based Optimization Algorithm for Solving Sylvester Matrix Equation

被引：4
|
作者：
Zhang, Juan [1 ]
Luo, Xiao [2 ]
机构：
[1] Xiangtan Univ, Key Lab Intelligent Comp & Informat Proc, Minist Educ, Xiangtan 411105, Peoples R China
[2] Xiangtan Univ, Hunan Key Lab Computat & Simulat Sci & Engn, Xiangtan 411105, Peoples R China
来源：
MATHEMATICS | 2022年 / 10卷 / 07期
基金：
中国国家自然科学基金;
关键词：
Sylvester matrix equation; Kronecker product; adaptive accelerated proximal gradient method; Newton-accelerated proximal gradient method; BLOCK ARNOLDI METHOD; APPROXIMATE SOLUTIONS; GMRES; FOM;
D O I：
10.3390/math10071040
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we transform the problem of solving the Sylvester matrix equation into an optimization problem through the Kronecker product primarily. We utilize the adaptive accelerated proximal gradient and Newton accelerated proximal gradient methods to solve the constrained non-convex minimization problem. Their convergent properties are analyzed. Finally, we offer numerical examples to illustrate the effectiveness of the derived algorithms.
引用
收藏
页数：14
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