An Iterative Algorithm for the Reflexive Solution of the General Coupled Matrix Equations
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 solut...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
|
| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2013/952974 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832562916390338560 |
|---|---|
| author | Zhongli Zhou Guangxin Huang |
| author_facet | Zhongli Zhou Guangxin Huang |
| author_sort | Zhongli Zhou |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-edc57c55a14e4f4cb8e2793be6110075 |
| institution | Kabale University |
| issn | 1537-744X |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-edc57c55a14e4f4cb8e2793be61100752025-02-03T01:21:30ZengWileyThe Scientific World Journal1537-744X2013-01-01201310.1155/2013/952974952974An Iterative Algorithm for the Reflexive Solution of the General Coupled Matrix EquationsZhongli Zhou0Guangxin Huang1Geomathematics Key Laboratory of Sichuan Province, College of Management Science, Chengdu University of Technology, Chengdu 610059, ChinaGeomathematics Key Laboratory of Sichuan Province, College of Management Science, Chengdu University of Technology, Chengdu 610059, ChinaThe 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.http://dx.doi.org/10.1155/2013/952974 |
| spellingShingle | Zhongli Zhou Guangxin Huang An Iterative Algorithm for the Reflexive Solution of the General Coupled Matrix Equations The Scientific World Journal |
| title | An Iterative Algorithm for the Reflexive Solution of the General Coupled Matrix Equations |
| title_full | An Iterative Algorithm for the Reflexive Solution of the General Coupled Matrix Equations |
| title_fullStr | An Iterative Algorithm for the Reflexive Solution of the General Coupled Matrix Equations |
| title_full_unstemmed | An Iterative Algorithm for the Reflexive Solution of the General Coupled Matrix Equations |
| title_short | An Iterative Algorithm for the Reflexive Solution of the General Coupled Matrix Equations |
| title_sort | iterative algorithm for the reflexive solution of the general coupled matrix equations |
| url | http://dx.doi.org/10.1155/2013/952974 |
| work_keys_str_mv | AT zhonglizhou aniterativealgorithmforthereflexivesolutionofthegeneralcoupledmatrixequations AT guangxinhuang aniterativealgorithmforthereflexivesolutionofthegeneralcoupledmatrixequations AT zhonglizhou iterativealgorithmforthereflexivesolutionofthegeneralcoupledmatrixequations AT guangxinhuang iterativealgorithmforthereflexivesolutionofthegeneralcoupledmatrixequations |