Paper Info
Title
The generalised Sylvester matrix equations over the generalised bisymmetric and skew-symmetric matrices
Abstract
A matrix P is called a symmetric orthogonal if P = PT = P−1. A matrix X is said to be a generalised bisymmetric with respect to P if X = XT = PXP. It is obvious that any symmetric matrix is also a generalised bisymmetric matrix with respect to I identity matrix. By extending the idea of the Jacobi and the Gauss–Seidel iterations, this article proposes two new iterative methods, respectively, for computing the generalised bisymmetric containing symmetric solution as a special case and skew-symmetric solutions of the generalised Sylvester matrix equation including Sylvester and Lyapunov matrix equations as special cases which is encountered in many systems and control applications. When the generalised Sylvester matrix equation has a unique generalised bisymmetric skew-symmetric solution, the first second iterative method converges to the generalised bisymmetric skew-symmetric solution of this matrix equation for any initial generalised bisymmetric skew-symmetric matrix. Finally, some numerical results are given to illustrate the effect of the theoretical results.
Year
DOI
Venue
2012
10.1080/00207721.2010.549584
Int. J. Systems Science
Keywords
Field
DocType
skew-symmetric matrix,matrix p,generalised bisymmetric matrix,special case,matrix equation,lyapunov matrix equation,matrix x,generalised bisymmetric,identity matrix,generalised sylvester matrix equation,symmetric matrix,gauss seidel,iteration method,iterative method,skew symmetric matrix,convergence,symmetric matrices
Convergent matrix,Mathematical optimization,Skew-symmetric matrix,Nonnegative matrix,Matrix function,Symmetric matrix,Sylvester matrix,Bisymmetric matrix,Mathematics,Centrosymmetric matrix
Journal
Volume
Issue
ISSN
43
8
0020-7721
Citations 
PageRank 
References 
16
0.61
20
Authors
2
Name
Order
Citations
PageRank
Mehdi Dehghan13022324.48
Masoud Hajarian234524.18