文章基本信息

标题：Matrix iteration algorithms for solving the generalized Lyapunov matrix equation
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作者：Juan Zhang ; Huihui Kang ; Shifeng Li 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2021
卷号：2021
期号：1
页码：1
DOI：10.1186/s13662-021-03381-1
出版社：Hindawi Publishing Corporation
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.
关键词：Generalized Lyapunov equation ; Cayley transformation ; BICR algorithm ; Bi-CGSTAB algorithm ; CRS algorithm