Iterative Methods to Solve the Generalized Coupled Sylvester-Conjugate Matrix Equations for Obtaining the Centrally Symmetric (Centrally Antisymmetric) Matrix Solutions
The iterative method is presented for obtaining the centrally symmetric (centrally antisymmetric) matrix pair (X,Y) solutions of the generalized coupled Sylvester-conjugate matrix equations A1X+B1Y=D1X¯E1+F1, A2Y+B2X=D2Y¯E2+F2. On the condition that the coupled matrix equations are consistent, we sh...
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/515816 |
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| author | Yajun Xie Changfeng Ma |
| author_facet | Yajun Xie Changfeng Ma |
| author_sort | Yajun Xie |
| collection | DOAJ |
| description | The iterative method is presented for obtaining the centrally symmetric (centrally antisymmetric) matrix pair (X,Y) solutions of the generalized coupled Sylvester-conjugate matrix equations A1X+B1Y=D1X¯E1+F1, A2Y+B2X=D2Y¯E2+F2. On the condition that the coupled matrix equations are consistent, we show that the solution pair (X*,Y*) can be obtained within finite iterative steps in the absence of round-off error for any initial value given centrally symmetric (centrally antisymmetric) matrix. Moreover, by choosing appropriate initial value, we can get the least Frobenius norm solution for the new generalized coupled Sylvester-conjugate linear matrix equations. Finally, some numerical examples are given to illustrate that the proposed iterative method is quite efficient. |
| format | Article |
| id | doaj-art-cad20f3232c645baa1de8f488a7aea0f |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-cad20f3232c645baa1de8f488a7aea0f2025-02-03T05:47:43ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/515816515816Iterative Methods to Solve the Generalized Coupled Sylvester-Conjugate Matrix Equations for Obtaining the Centrally Symmetric (Centrally Antisymmetric) Matrix SolutionsYajun Xie0Changfeng Ma1School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007, ChinaSchool of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007, ChinaThe iterative method is presented for obtaining the centrally symmetric (centrally antisymmetric) matrix pair (X,Y) solutions of the generalized coupled Sylvester-conjugate matrix equations A1X+B1Y=D1X¯E1+F1, A2Y+B2X=D2Y¯E2+F2. On the condition that the coupled matrix equations are consistent, we show that the solution pair (X*,Y*) can be obtained within finite iterative steps in the absence of round-off error for any initial value given centrally symmetric (centrally antisymmetric) matrix. Moreover, by choosing appropriate initial value, we can get the least Frobenius norm solution for the new generalized coupled Sylvester-conjugate linear matrix equations. Finally, some numerical examples are given to illustrate that the proposed iterative method is quite efficient.http://dx.doi.org/10.1155/2014/515816 |
| spellingShingle | Yajun Xie Changfeng Ma Iterative Methods to Solve the Generalized Coupled Sylvester-Conjugate Matrix Equations for Obtaining the Centrally Symmetric (Centrally Antisymmetric) Matrix Solutions Journal of Applied Mathematics |
| title | Iterative Methods to Solve the Generalized Coupled Sylvester-Conjugate Matrix Equations for Obtaining the Centrally Symmetric (Centrally Antisymmetric) Matrix Solutions |
| title_full | Iterative Methods to Solve the Generalized Coupled Sylvester-Conjugate Matrix Equations for Obtaining the Centrally Symmetric (Centrally Antisymmetric) Matrix Solutions |
| title_fullStr | Iterative Methods to Solve the Generalized Coupled Sylvester-Conjugate Matrix Equations for Obtaining the Centrally Symmetric (Centrally Antisymmetric) Matrix Solutions |
| title_full_unstemmed | Iterative Methods to Solve the Generalized Coupled Sylvester-Conjugate Matrix Equations for Obtaining the Centrally Symmetric (Centrally Antisymmetric) Matrix Solutions |
| title_short | Iterative Methods to Solve the Generalized Coupled Sylvester-Conjugate Matrix Equations for Obtaining the Centrally Symmetric (Centrally Antisymmetric) Matrix Solutions |
| title_sort | iterative methods to solve the generalized coupled sylvester conjugate matrix equations for obtaining the centrally symmetric centrally antisymmetric matrix solutions |
| url | http://dx.doi.org/10.1155/2014/515816 |
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