Iterative Algorithm for Solving a Class of Quaternion Matrix Equation over the Generalized (P,Q)-Reflexive Matrices
The matrix equation ∑l=1uAlXBl+∑s=1vCsXTDs=F, which includes some frequently investigated matrix equations as its special cases, plays important roles in the system theory. In this paper, we propose an iterative algorithm for solving the quaternion matrix equation ∑l=1uAlXBl+∑s=1vCsXTDs=F over gener...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/831656 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850228221392453632 |
|---|---|
| author | Ning Li Qing-Wen Wang |
| author_facet | Ning Li Qing-Wen Wang |
| author_sort | Ning Li |
| collection | DOAJ |
| description | The matrix equation ∑l=1uAlXBl+∑s=1vCsXTDs=F, which includes some frequently investigated matrix equations as its special cases, plays important roles in the system theory. In this paper, we propose an iterative algorithm for solving the quaternion matrix equation ∑l=1uAlXBl+∑s=1vCsXTDs=F over generalized (P,Q)-reflexive matrices. The proposed iterative algorithm automatically determines the solvability of the quaternion matrix equation over generalized (P,Q)-reflexive matrices. When the matrix equation is consistent over generalized (P,Q)-reflexive matrices, the sequence {X(k)} generated by the introduced algorithm converges to a generalized (P,Q)-reflexive solution of the quaternion matrix equation. And the sequence {X(k)} converges to the least Frobenius norm generalized (P,Q)-reflexive solution of the quaternion matrix equation when an appropriate initial iterative matrix is chosen. Furthermore, the optimal approximate generalized (P,Q)-reflexive solution for a given generalized (P,Q)-reflexive matrix X0 can be derived. The numerical results indicate that the iterative algorithm is quite efficient. |
| format | Article |
| id | doaj-art-232a8c73af4a4fce9135fc67cfe31e6b |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-232a8c73af4a4fce9135fc67cfe31e6b2025-08-20T02:04:35ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/831656831656Iterative Algorithm for Solving a Class of Quaternion Matrix Equation over the Generalized (P,Q)-Reflexive MatricesNing Li0Qing-Wen Wang1School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Jinan, Shandong Province 250002, ChinaDepartment of Mathematics, Shanghai University, Shanghai 200444, ChinaThe matrix equation ∑l=1uAlXBl+∑s=1vCsXTDs=F, which includes some frequently investigated matrix equations as its special cases, plays important roles in the system theory. In this paper, we propose an iterative algorithm for solving the quaternion matrix equation ∑l=1uAlXBl+∑s=1vCsXTDs=F over generalized (P,Q)-reflexive matrices. The proposed iterative algorithm automatically determines the solvability of the quaternion matrix equation over generalized (P,Q)-reflexive matrices. When the matrix equation is consistent over generalized (P,Q)-reflexive matrices, the sequence {X(k)} generated by the introduced algorithm converges to a generalized (P,Q)-reflexive solution of the quaternion matrix equation. And the sequence {X(k)} converges to the least Frobenius norm generalized (P,Q)-reflexive solution of the quaternion matrix equation when an appropriate initial iterative matrix is chosen. Furthermore, the optimal approximate generalized (P,Q)-reflexive solution for a given generalized (P,Q)-reflexive matrix X0 can be derived. The numerical results indicate that the iterative algorithm is quite efficient.http://dx.doi.org/10.1155/2013/831656 |
| spellingShingle | Ning Li Qing-Wen Wang Iterative Algorithm for Solving a Class of Quaternion Matrix Equation over the Generalized (P,Q)-Reflexive Matrices Abstract and Applied Analysis |
| title | Iterative Algorithm for Solving a Class of Quaternion Matrix Equation over the Generalized (P,Q)-Reflexive Matrices |
| title_full | Iterative Algorithm for Solving a Class of Quaternion Matrix Equation over the Generalized (P,Q)-Reflexive Matrices |
| title_fullStr | Iterative Algorithm for Solving a Class of Quaternion Matrix Equation over the Generalized (P,Q)-Reflexive Matrices |
| title_full_unstemmed | Iterative Algorithm for Solving a Class of Quaternion Matrix Equation over the Generalized (P,Q)-Reflexive Matrices |
| title_short | Iterative Algorithm for Solving a Class of Quaternion Matrix Equation over the Generalized (P,Q)-Reflexive Matrices |
| title_sort | iterative algorithm for solving a class of quaternion matrix equation over the generalized p q reflexive matrices |
| url | http://dx.doi.org/10.1155/2013/831656 |
| work_keys_str_mv | AT ningli iterativealgorithmforsolvingaclassofquaternionmatrixequationoverthegeneralizedpqreflexivematrices AT qingwenwang iterativealgorithmforsolvingaclassofquaternionmatrixequationoverthegeneralizedpqreflexivematrices |