Paper Info
Title
The accelerated gradient based iterative algorithm for solving a class of generalized Sylvester-transpose matrix equation
Abstract
In this paper, we present an accelerated gradient based algorithm by minimizing certain criterion quadratic function for solving the generalized Sylvester-transpose matrix equation AXB + CXT D = F. The idea is from (Ding and Chen, 2005; Niu et al., 2011; Wang et al., 2012) in which some efficient algorithms were developed for solving the Sylvester matrix equation and the Lyapunov matrix equation. On the basis of the information generated in the previous half-step, we further introduce a relaxation factor to obtain the solution of the generalized Sylvester-transpose matrix equation. We show that the iterative solution converges to the exact solution for any initial value provided that some appropriate assumptions. Finally, some numerical examples are given to illustrate that the introduced iterative algorithm is efficient. (C) 2015 Elsevier Inc. All rights reserved.
Year
DOI
Venue
2016
10.1016/j.amc.2015.07.022
Applied Mathematics and Computation
Keywords
Field
DocType
Generalized Sylvester-transpose matrix equation,Accelerated gradient based iterative (AGBI) algorithm,Relaxation factor,Numerical test
Convergent matrix,Mathematical optimization,Equation solving,Sylvester equation,Mathematical analysis,Iterative method,Matrix difference equation,Sylvester's law of inertia,Sylvester matrix,Matrix differential equation,Mathematics
Journal
Volume
ISSN
Citations 
273
0096-3003
8
PageRank 
References 
Authors
0.44
30
2
Name
Order
Citations
PageRank
Yajun Xie1120.84
Changfeng Ma219729.63