An Iterative Algorithm for the Reflexive Solution of the General Coupled Matrix Equations
Joint Authors
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-11-11
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Medicine
Information Technology and Computer Science
Abstract EN
The general coupled matrix equations (including the generalized coupled Sylvester matrix equations as special cases) have numerous applications in control and system theory.
In this paper, an iterative algorithm is constructed to solve the general coupled matrix equations over reflexive matrix solution.
When the general coupled matrix equations are consistent over reflexive matrices, the reflexive solution can be determined automatically by the iterative algorithm within finite iterative steps in the absence of round-off errors.
The least Frobenius norm reflexive solution of the general coupled matrix equations can be derived when an appropriate initial matrix is chosen.
Furthermore, the unique optimal approximation reflexive solution to a given matrix group in Frobenius norm can be derived by finding the least-norm reflexive solution of the corresponding general coupled matrix equations.
A numerical example is given to illustrate the effectiveness of the proposed iterative algorithm.
American Psychological Association (APA)
Zhou, Zhongli& Huang, Guang-Xin. 2013. An Iterative Algorithm for the Reflexive Solution of the General Coupled Matrix Equations. The Scientific World Journal،Vol. 2013, no. 2013, pp.1-15.
https://search.emarefa.net/detail/BIM-1013212
Modern Language Association (MLA)
Zhou, Zhongli& Huang, Guang-Xin. An Iterative Algorithm for the Reflexive Solution of the General Coupled Matrix Equations. The Scientific World Journal No. 2013 (2013), pp.1-15.
https://search.emarefa.net/detail/BIM-1013212
American Medical Association (AMA)
Zhou, Zhongli& Huang, Guang-Xin. An Iterative Algorithm for the Reflexive Solution of the General Coupled Matrix Equations. The Scientific World Journal. 2013. Vol. 2013, no. 2013, pp.1-15.
https://search.emarefa.net/detail/BIM-1013212
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1013212