The Hermitian -Conjugate Generalized Procrustes Problem
We consider the Hermitian -conjugate generalized Procrustes problem to find Hermitian -conjugate matrix such that is minimum, where , , , and (, ) are given complex matrices, and and are positive integers. The expression of the solution to Hermitian -conjugate generalized Procrustes problem is...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/423605 |
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| author | Hai-Xia Chang Xue-Feng Duan Qing-Wen Wang |
| author_facet | Hai-Xia Chang Xue-Feng Duan Qing-Wen Wang |
| author_sort | Hai-Xia Chang |
| collection | DOAJ |
| description | We consider the Hermitian -conjugate generalized Procrustes problem to find Hermitian -conjugate matrix such that is minimum, where , , , and (, ) are given complex matrices, and and are positive integers. The expression of the solution to Hermitian -conjugate generalized Procrustes problem is derived. And the optimal approximation solution in the solution set for Hermitian -conjugate generalized Procrustes problem to a given matrix is also obtained. Furthermore, we establish necessary and sufficient conditions for the existence and the formula for Hermitian -conjugate solution to the linear system of complex matrix equations , , ( and are positive integers). The representation of the corresponding optimal approximation problem is presented. Finally, an algorithm for solving two problems above is proposed, and the numerical examples show its feasibility. |
| format | Article |
| id | doaj-art-f6157fb43b044f4d8d39bba88a79c17e |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-f6157fb43b044f4d8d39bba88a79c17e2025-02-03T01:30:49ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/423605423605The Hermitian -Conjugate Generalized Procrustes ProblemHai-Xia Chang0Xue-Feng Duan1Qing-Wen Wang2Department of Applied Mathematics, Shanghai Finance University, Shanghai 201209, ChinaSchool of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin 541004, ChinaDepartment of Mathematics, Shanghai University, Shanghai 200444, ChinaWe consider the Hermitian -conjugate generalized Procrustes problem to find Hermitian -conjugate matrix such that is minimum, where , , , and (, ) are given complex matrices, and and are positive integers. The expression of the solution to Hermitian -conjugate generalized Procrustes problem is derived. And the optimal approximation solution in the solution set for Hermitian -conjugate generalized Procrustes problem to a given matrix is also obtained. Furthermore, we establish necessary and sufficient conditions for the existence and the formula for Hermitian -conjugate solution to the linear system of complex matrix equations , , ( and are positive integers). The representation of the corresponding optimal approximation problem is presented. Finally, an algorithm for solving two problems above is proposed, and the numerical examples show its feasibility.http://dx.doi.org/10.1155/2013/423605 |
| spellingShingle | Hai-Xia Chang Xue-Feng Duan Qing-Wen Wang The Hermitian -Conjugate Generalized Procrustes Problem Abstract and Applied Analysis |
| title | The Hermitian -Conjugate Generalized Procrustes Problem |
| title_full | The Hermitian -Conjugate Generalized Procrustes Problem |
| title_fullStr | The Hermitian -Conjugate Generalized Procrustes Problem |
| title_full_unstemmed | The Hermitian -Conjugate Generalized Procrustes Problem |
| title_short | The Hermitian -Conjugate Generalized Procrustes Problem |
| title_sort | hermitian conjugate generalized procrustes problem |
| url | http://dx.doi.org/10.1155/2013/423605 |
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