LSMR Iterative Method for General Coupled Matrix Equations
By extending the idea of LSMR method, we present an iterative method to solve the general coupled matrix equations ∑k=1qAikXkBik=Ci, i=1,2,…,p, (including the generalized (coupled) Lyapunov and Sylvester matrix equations as special cases) over some constrained matrix groups (X1,X2,…,Xq), such as sym...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2015/562529 |
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| author | F. Toutounian D. Khojasteh Salkuyeh M. Mojarrab |
| author_facet | F. Toutounian D. Khojasteh Salkuyeh M. Mojarrab |
| author_sort | F. Toutounian |
| collection | DOAJ |
| description | By extending the idea of LSMR method, we present an iterative method to solve the general coupled matrix equations ∑k=1qAikXkBik=Ci, i=1,2,…,p, (including the generalized (coupled) Lyapunov and Sylvester matrix equations as special cases) over some constrained matrix groups (X1,X2,…,Xq), such as symmetric, generalized bisymmetric, and (R,S)-symmetric matrix groups. By this iterative method, for any initial matrix group (X1(0),X2(0),…,Xq(0)), a solution group (X1*,X2*,…,Xq*) can be obtained within finite iteration steps in absence of round-off errors, and the minimum Frobenius norm solution or the minimum Frobenius norm least-squares solution group can be derived when an appropriate initial iterative matrix group is chosen. In addition, the optimal approximation solution group to a given matrix group (X¯1,X¯2,…,X¯q) in the Frobenius norm can be obtained by finding the least Frobenius norm solution group of new general coupled matrix equations. Finally, numerical examples are given to illustrate the effectiveness of the presented method. |
| format | Article |
| id | doaj-art-99a1d5edd6b641f5a5fa9aff5360f72a |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-99a1d5edd6b641f5a5fa9aff5360f72a2025-08-20T03:36:48ZengWileyJournal of Applied Mathematics1110-757X1687-00422015-01-01201510.1155/2015/562529562529LSMR Iterative Method for General Coupled Matrix EquationsF. Toutounian0D. Khojasteh Salkuyeh1M. Mojarrab2Department of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, IranFaculty of Mathematical Sciences, University of Guilan, IranDepartment of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, IranBy extending the idea of LSMR method, we present an iterative method to solve the general coupled matrix equations ∑k=1qAikXkBik=Ci, i=1,2,…,p, (including the generalized (coupled) Lyapunov and Sylvester matrix equations as special cases) over some constrained matrix groups (X1,X2,…,Xq), such as symmetric, generalized bisymmetric, and (R,S)-symmetric matrix groups. By this iterative method, for any initial matrix group (X1(0),X2(0),…,Xq(0)), a solution group (X1*,X2*,…,Xq*) can be obtained within finite iteration steps in absence of round-off errors, and the minimum Frobenius norm solution or the minimum Frobenius norm least-squares solution group can be derived when an appropriate initial iterative matrix group is chosen. In addition, the optimal approximation solution group to a given matrix group (X¯1,X¯2,…,X¯q) in the Frobenius norm can be obtained by finding the least Frobenius norm solution group of new general coupled matrix equations. Finally, numerical examples are given to illustrate the effectiveness of the presented method.http://dx.doi.org/10.1155/2015/562529 |
| spellingShingle | F. Toutounian D. Khojasteh Salkuyeh M. Mojarrab LSMR Iterative Method for General Coupled Matrix Equations Journal of Applied Mathematics |
| title | LSMR Iterative Method for General Coupled Matrix Equations |
| title_full | LSMR Iterative Method for General Coupled Matrix Equations |
| title_fullStr | LSMR Iterative Method for General Coupled Matrix Equations |
| title_full_unstemmed | LSMR Iterative Method for General Coupled Matrix Equations |
| title_short | LSMR Iterative Method for General Coupled Matrix Equations |
| title_sort | lsmr iterative method for general coupled matrix equations |
| url | http://dx.doi.org/10.1155/2015/562529 |
| work_keys_str_mv | AT ftoutounian lsmriterativemethodforgeneralcoupledmatrixequations AT dkhojastehsalkuyeh lsmriterativemethodforgeneralcoupledmatrixequations AT mmojarrab lsmriterativemethodforgeneralcoupledmatrixequations |