The Alternating Direction Methods for Solving the Sylvester-Type Matrix Equation $AXB+CX^⊤D=E$

The Alternating Direction Methods for Solving the Sylvester-Type Matrix Equation $AXB+CX^⊤D=E$

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.

Author Details

Yifen Ke

Changfeng Ma