Paper Info
Title
An iterative method for the symmetric and skew symmetric solutions of a linear matrix equation AXB+CYD=E
Abstract
In this paper, two efficient iterative methods are presented to solve the symmetric and skew symmetric solutions of a linear matrix equation AXB+CYD=E, respectively, with real pair matrices X and Y. By these two iterative methods, the solvability of the symmetric and skew symmetric solutions for the matrix equation can be determined automatically. When the matrix equation has symmetric and skew symmetric solutions, then, for any initial pair matrices X"0 and Y"0, symmetric and skew symmetric solutions can be obtained within finite iteration steps in the absence of roundoff errors, and the minimum norm of the symmetric and skew symmetric solutions can be obtained by choosing a special kind of initial pair matrices. In addition, the unique optimal approximation pair solution X@^ and Y@^ to the given matrices X@? and Y@? in Frobenius norm can be obtained by finding the minimum norm solution of a new matrix equation AX@?B+CY@?D=E@?, where E@?=E-AX@?B-CY@?D. The given numerical examples demonstrate that the iterative methods are quite efficient.
Year
DOI
Venue
2010
10.1016/j.cam.2009.11.052
J. Computational Applied Mathematics
Keywords
Field
DocType
initial pair,linear matrix equation,matrix equation,real pair,skew symmetric solution,solution x,initial pair matrix,matrices x,new matrix equation,iterative method,iteration method
Symmetric function,Mathematical optimization,Skew-symmetric matrix,Power sum symmetric polynomial,Elementary symmetric polynomial,Mathematical analysis,Ring of symmetric functions,Triple system,Symmetric closure,Complete homogeneous symmetric polynomial,Mathematics
Journal
Volume
Issue
ISSN
233
11
0377-0427
Citations 
PageRank 
References 
10
0.84
7
Authors
2
Name
Order
Citations
PageRank
Xingping Sheng1656.82
Guo-Liang Chen210617.84