Paper Info
Title
The modified conjugate gradient methods for solving a class of generalized coupled Sylvester-transpose matrix equations.
Abstract
In this paper, we consider the iteration solutions of generalized coupled Sylvester-transpose matrix equations: A1XB1+C1YTD1=F1, A2YB2+C2XTD2=F2. When the coupled matrix equations are consistent, we propose a modified conjugate gradient method to solve the equations and prove that a solution (X∗,Y∗) can be obtained within finite iterative steps in the absence of roundoff-error for any initial value. Furthermore, we show that the minimum-norm solution can be got by choosing a special kind of initial matrices. When the coupled matrix equations are inconsistent, we present another modified conjugate gradient method to find the least-squares solution with the minimum-norm. Finally, some numerical examples are given to show the behavior of the considered algorithms.
Year
DOI
Venue
2014
10.1016/j.camwa.2014.02.003
Computers & Mathematics with Applications
Keywords
Field
DocType
Generalized coupled Sylvester-transpose matrix equations,Modified conjugate gradient method,Minimum-norm solution,Least-squares solution,Numerical experiment
Conjugate gradient method,Mathematical optimization,Mathematical analysis,Matrix (mathematics),Nonlinear conjugate gradient method,Hermitian matrix,Mathematics,Biconjugate gradient method,Derivation of the conjugate gradient method,Conjugate transpose,Conjugate residual method
Journal
Volume
Issue
ISSN
67
8
0898-1221
Citations 
PageRank 
References 
16
0.61
22
Authors
2
Name
Order
Citations
PageRank
Na Huang1243.53
Changfeng Ma210016.25