An Iterative Algorithm for the Generalized Reflexive Solution of the Matrix Equations AXB=E, CXD=F
An iterative algorithm is constructed to solve the linear matrix equation pair AXB=E, CXD=F over generalized reflexive matrix X. When the matrix equation pair AXB=E, CXD=F is consistent over generalized reflexive matrix X, for any generalized reflexive initial iterative matrix X1, the generalized re...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/492951 |
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| author | Deqin Chen Feng Yin Guang-Xin Huang |
| author_facet | Deqin Chen Feng Yin Guang-Xin Huang |
| author_sort | Deqin Chen |
| collection | DOAJ |
| description | An iterative algorithm is constructed to solve the linear matrix equation pair AXB=E, CXD=F over generalized reflexive matrix X. When the matrix equation pair AXB=E, CXD=F is consistent over generalized reflexive matrix X, for any generalized reflexive initial iterative matrix X1, the generalized reflexive solution can be obtained by the iterative algorithm within finite iterative steps in the absence of round-off errors. The unique least-norm generalized reflexive iterative solution of the matrix equation pair can be derived when an appropriate initial iterative matrix is chosen. Furthermore, the optimal approximate solution of AXB=E, CXD=F for a given generalized reflexive matrix X0 can be derived by finding the least-norm generalized reflexive solution of a new corresponding matrix equation pair AX̃B=Ẽ, CX̃D=F̃ with Ẽ=E-AX0B, F̃=F-CX0D. Finally, several numerical examples are given to illustrate that our iterative algorithm is effective. |
| format | Article |
| id | doaj-art-b7bf759baa7a4215ba2badaca1db55e4 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-b7bf759baa7a4215ba2badaca1db55e42025-02-03T07:25:04ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/492951492951An Iterative Algorithm for the Generalized Reflexive Solution of the Matrix Equations AXB=E, CXD=FDeqin Chen0Feng Yin1Guang-Xin Huang2School of Science, Sichuan University of Science and Engineering, Zigong 643000, ChinaSchool of Science, Sichuan University of Science and Engineering, Zigong 643000, ChinaCollege of Management Science, Key Laboratory of Geomathematics in Sichuan, Chengdu University of Technology, Chengdu 610059, ChinaAn iterative algorithm is constructed to solve the linear matrix equation pair AXB=E, CXD=F over generalized reflexive matrix X. When the matrix equation pair AXB=E, CXD=F is consistent over generalized reflexive matrix X, for any generalized reflexive initial iterative matrix X1, the generalized reflexive solution can be obtained by the iterative algorithm within finite iterative steps in the absence of round-off errors. The unique least-norm generalized reflexive iterative solution of the matrix equation pair can be derived when an appropriate initial iterative matrix is chosen. Furthermore, the optimal approximate solution of AXB=E, CXD=F for a given generalized reflexive matrix X0 can be derived by finding the least-norm generalized reflexive solution of a new corresponding matrix equation pair AX̃B=Ẽ, CX̃D=F̃ with Ẽ=E-AX0B, F̃=F-CX0D. Finally, several numerical examples are given to illustrate that our iterative algorithm is effective.http://dx.doi.org/10.1155/2012/492951 |
| spellingShingle | Deqin Chen Feng Yin Guang-Xin Huang An Iterative Algorithm for the Generalized Reflexive Solution of the Matrix Equations AXB=E, CXD=F Journal of Applied Mathematics |
| title | An Iterative Algorithm for the Generalized Reflexive Solution of the Matrix Equations AXB=E, CXD=F |
| title_full | An Iterative Algorithm for the Generalized Reflexive Solution of the Matrix Equations AXB=E, CXD=F |
| title_fullStr | An Iterative Algorithm for the Generalized Reflexive Solution of the Matrix Equations AXB=E, CXD=F |
| title_full_unstemmed | An Iterative Algorithm for the Generalized Reflexive Solution of the Matrix Equations AXB=E, CXD=F |
| title_short | An Iterative Algorithm for the Generalized Reflexive Solution of the Matrix Equations AXB=E, CXD=F |
| title_sort | iterative algorithm for the generalized reflexive solution of the matrix equations axb e cxd f |
| url | http://dx.doi.org/10.1155/2012/492951 |
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