Matrix iteration algorithms for solving the generalized Lyapunov matrix equation

被引：2
|
作者：
Zhang, Juan [1 ]
Kang, Huihui [1 ]
Li, Shifeng [1 ]
机构：
[1] Xiangtan Univ, Dept Math & Computat Sci, Hunan Key Lab Computat & Simulat Sci & Engn, Xiangtan, Hunan, Peoples R China
来源：
ADVANCES IN DIFFERENCE EQUATIONS | 2021年 / 2021卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Generalized Lyapunov equation; Cayley transformation; BICR algorithm; Bi-CGSTAB algorithm; CRS algorithm; PROJECTION METHOD; BI-CG; REDUCTION;
D O I：
10.1186/s13662-021-03381-1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we first recall some well-known results on the solvability of the generalized Lyapunov equation and rewrite this equation into the generalized Stein equation by using Cayley transformation. Then we introduce the matrix versions of biconjugate residual (BICR), biconjugate gradients stabilized (Bi-CGSTAB), and conjugate residual squared (CRS) algorithms. This study's primary motivation is to avoid the increase of computational complexity by using the Kronecker product and vectorization operation. Finally, we offer several numerical examples to show the effectiveness of the derived algorithms.
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收藏
页数：18
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