THE ALTERNATING DIRECTION METHODS FOR SOLVING THE SYLVESTER-TYPE MATRIX EQUATION AXB + CXTD =E

• 来源期刊: 计算数学（英文版）
• 关键词: Sylvester-type matrix equation Alternating direction method The least squares solution Best approximate solution
• 年，卷（期）: 2017,（5）
• 页码范围: 620-641
• 页数: 22页
• 语种: 英文
• DOI: 10.4208/jcm.1608-m2015-0430

摘要

In this paper,we present two alternating direction methods for the solution and best approximate solution of the Sylvester-type matrix equation AXB + CXTD =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.