An Iterative Algorithm for the Generalized Reflexive Solutions of the Generalized Coupled Sylvester Matrix Equations
Joint Authors
Source
Journal of Applied Mathematics
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-28, 28 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-08-26
Country of Publication
Egypt
No. of Pages
28
Main Subjects
Abstract EN
An iterative algorithm is constructed to solve the generalized coupled Sylvester matrix equations (AXB-CYD,EXF-GYH)=(M,N), which includes Sylvester and Lyapunov matrix equations as special cases, over generalized reflexive matrices X and Y.
When the matrix equations are consistent, for any initial generalized reflexive matrix pair [X1,Y1], the generalized reflexive solutions can be obtained by the iterative algorithm within finite iterative steps in the absence of round-off errors, and the least Frobenius norm generalized reflexive solutions can be obtained by choosing a special kind of initial matrix pair.
The unique optimal approximation generalized reflexive solution pair [X̂,Ŷ] to a given matrix pair [X0,Y0] in Frobenius norm can be derived by finding the least-norm generalized reflexive solution pair [X̃*,Ỹ*] of a new corresponding generalized coupled Sylvester matrix equation pair (AX̃B-CỸD,EX̃F-GỸH)=(M̃,Ñ), where M̃=M-AX0B+CY0D,Ñ=N-EX0F+GY0H.
Several numerical examples are given to show the effectiveness of the presented iterative algorithm.
American Psychological Association (APA)
Yin, Feng& Huang, Guang-Xin. 2012. An Iterative Algorithm for the Generalized Reflexive Solutions of the Generalized Coupled Sylvester Matrix Equations. Journal of Applied Mathematics،Vol. 2012, no. 2012, pp.1-28.
https://search.emarefa.net/detail/BIM-992981
Modern Language Association (MLA)
Yin, Feng& Huang, Guang-Xin. An Iterative Algorithm for the Generalized Reflexive Solutions of the Generalized Coupled Sylvester Matrix Equations. Journal of Applied Mathematics No. 2012 (2012), pp.1-28.
https://search.emarefa.net/detail/BIM-992981
American Medical Association (AMA)
Yin, Feng& Huang, Guang-Xin. An Iterative Algorithm for the Generalized Reflexive Solutions of the Generalized Coupled Sylvester Matrix Equations. Journal of Applied Mathematics. 2012. Vol. 2012, no. 2012, pp.1-28.
https://search.emarefa.net/detail/BIM-992981
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-992981