![](/images/graphics-bg.png)
An Iterative Algorithm for the Least Squares Generalized Reflexive Solutions of the Matrix Equations AXB=E,CXD=F
Joint Authors
Source
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-18, 18 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-03-12
Country of Publication
Egypt
No. of Pages
18
Main Subjects
Abstract EN
The generalized coupled Sylvester systems play a fundamental role in wide applications in several areas, such as stability theory, control theory, perturbation analysis, and some other fields of pure and applied mathematics.
The iterative method is an important way to solve the generalized coupled Sylvester systems.
In this paper, an iterative algorithm is constructed to solve the minimum Frobenius norm residual problem: ‖(AXBCXD)-(EF)‖= min over generalized reflexive matrix X.
For any initial generalized reflexive matrix X1, by the iterative algorithm, the generalized reflexive solution X* can be obtained within finite iterative steps in the absence of round-off errors, and the unique least-norm generalized reflexive solution X* can also be derived when an appropriate initial iterative matrix is chosen.
Furthermore, the unique optimal approximate solution X^ to a given matrix X0 in Frobenius norm can be derived by finding the least-norm generalized reflexive solution X~* of a new corresponding minimum Frobenius norm residual problem: min‖(AX~BCX~D)-(E~F~)‖ with E~=E-AX0B, F~=F-CX0D.
Finally, several numerical examples are given to illustrate that our iterative algorithm is effective.
American Psychological Association (APA)
Yin, Feng& Huang, Guang-Xin. 2012. An Iterative Algorithm for the Least Squares Generalized Reflexive Solutions of the Matrix Equations AXB=E,CXD=F. Abstract and Applied Analysis،Vol. 2012, no. 2012, pp.1-18.
https://search.emarefa.net/detail/BIM-503807
Modern Language Association (MLA)
Yin, Feng& Huang, Guang-Xin. An Iterative Algorithm for the Least Squares Generalized Reflexive Solutions of the Matrix Equations AXB=E,CXD=F. Abstract and Applied Analysis No. 2012 (2012), pp.1-18.
https://search.emarefa.net/detail/BIM-503807
American Medical Association (AMA)
Yin, Feng& Huang, Guang-Xin. An Iterative Algorithm for the Least Squares Generalized Reflexive Solutions of the Matrix Equations AXB=E,CXD=F. Abstract and Applied Analysis. 2012. Vol. 2012, no. 2012, pp.1-18.
https://search.emarefa.net/detail/BIM-503807
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-503807