Procrustes Problems for General, Triangular, and Symmetric Toeplitz Matrices
The Toeplitz Procrustes problems are the least squares problems for the matrix equation AX=B over some Toeplitz matrix sets. In this paper the necessary and sufficient conditions are obtained about the existence and uniqueness for the solutions of the Toeplitz Procrustes problems when the unknown ma...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/696019 |
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| _version_ | 1832565486486814720 |
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| author | Juan Yang Yuan-bei Deng |
| author_facet | Juan Yang Yuan-bei Deng |
| author_sort | Juan Yang |
| collection | DOAJ |
| description | The Toeplitz Procrustes problems are the least squares problems for the matrix equation AX=B over some Toeplitz matrix sets. In this paper the necessary and sufficient conditions are obtained about the existence and uniqueness for the solutions of the Toeplitz Procrustes problems when the unknown matrices are constrained to the general, the triangular, and the symmetric Toeplitz matrices, respectively. The algorithms are designed and the numerical examples show that these algorithms are feasible. |
| format | Article |
| id | doaj-art-028a278677f14fce973a74b96b6919c3 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-028a278677f14fce973a74b96b6919c32025-02-03T01:07:23ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/696019696019Procrustes Problems for General, Triangular, and Symmetric Toeplitz MatricesJuan Yang0Yuan-bei Deng1College of Mathematics and Econometrics, Hunan University, Changsha, ChinaCollege of Mathematics and Econometrics, Hunan University, Changsha, ChinaThe Toeplitz Procrustes problems are the least squares problems for the matrix equation AX=B over some Toeplitz matrix sets. In this paper the necessary and sufficient conditions are obtained about the existence and uniqueness for the solutions of the Toeplitz Procrustes problems when the unknown matrices are constrained to the general, the triangular, and the symmetric Toeplitz matrices, respectively. The algorithms are designed and the numerical examples show that these algorithms are feasible.http://dx.doi.org/10.1155/2013/696019 |
| spellingShingle | Juan Yang Yuan-bei Deng Procrustes Problems for General, Triangular, and Symmetric Toeplitz Matrices Journal of Applied Mathematics |
| title | Procrustes Problems for General, Triangular, and Symmetric Toeplitz Matrices |
| title_full | Procrustes Problems for General, Triangular, and Symmetric Toeplitz Matrices |
| title_fullStr | Procrustes Problems for General, Triangular, and Symmetric Toeplitz Matrices |
| title_full_unstemmed | Procrustes Problems for General, Triangular, and Symmetric Toeplitz Matrices |
| title_short | Procrustes Problems for General, Triangular, and Symmetric Toeplitz Matrices |
| title_sort | procrustes problems for general triangular and symmetric toeplitz matrices |
| url | http://dx.doi.org/10.1155/2013/696019 |
| work_keys_str_mv | AT juanyang procrustesproblemsforgeneraltriangularandsymmetrictoeplitzmatrices AT yuanbeideng procrustesproblemsforgeneraltriangularandsymmetrictoeplitzmatrices |