Year: 2017
Author: Yifen Ke, Changfeng Ma
Journal of Computational Mathematics, Vol. 35 (2017), Iss. 5 : pp. 620–641
Abstract
In this paper, we present two alternating direction methods for the solution and best approximate solution of the Sylvester-type matrix equation $AXB+CX^⊤D=E$ arising in the control theory, where $A,B,C,D$ and $E$ are given matrices of suitable sizes. If the matrix equation is consistent (inconsistent), then the solution (the least squares solution) can be obtained. Preliminary convergence properties of the proposed algorithms are presented. Numerical experiments show that the proposed algorithms tend to deliver higher quality solutions with less iteration steps and CPU time than some existing algorithms on the tested problems.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1608-m2015-0430
Journal of Computational Mathematics, Vol. 35 (2017), Iss. 5 : pp. 620–641
Published online: 2017-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Sylvester-type matrix equation Alternating direction method The least squares solution Best approximate solution.