A Note on the Square Roots of a Class of Circulant Matrices
We prove that any k-circulant matrix and any even order skew k-circulant matrix are diagonalizable for any k∈ℂ. Then, we propose two algorithms for computing the square roots of the k-circulant matrix and the skew k-circulant matrix, respectively. In particular, we show that the square roots of the...
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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/10.1155/2013/601243 |
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| _version_ | 1832566619905196032 |
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| author | Ying Zhang Huisheng Zhang Guoyan Chen |
| author_facet | Ying Zhang Huisheng Zhang Guoyan Chen |
| author_sort | Ying Zhang |
| collection | DOAJ |
| description | We prove that any k-circulant matrix and any even order skew k-circulant matrix are diagonalizable for any k∈ℂ. Then, we propose two algorithms for computing the square roots of the k-circulant matrix and the skew k-circulant matrix, respectively. In particular, we show that the square roots of the k-circulant matrix are still k-circulant matrices. Both the theoretical analysis and the numerical experiments show that our algorithms are faster than the standard Schur method. |
| format | Article |
| id | doaj-art-6c306ac9059b41ab8245ef11c8568495 |
| 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-6c306ac9059b41ab8245ef11c85684952025-02-03T01:03:36ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/601243601243A Note on the Square Roots of a Class of Circulant MatricesYing Zhang0Huisheng Zhang1Guoyan Chen2Department of Mathematics, Dalian Maritime University, Dalian 116026, ChinaDepartment of Mathematics, Dalian Maritime University, Dalian 116026, ChinaDepartment of Mathematics, Dalian Maritime University, Dalian 116026, ChinaWe prove that any k-circulant matrix and any even order skew k-circulant matrix are diagonalizable for any k∈ℂ. Then, we propose two algorithms for computing the square roots of the k-circulant matrix and the skew k-circulant matrix, respectively. In particular, we show that the square roots of the k-circulant matrix are still k-circulant matrices. Both the theoretical analysis and the numerical experiments show that our algorithms are faster than the standard Schur method.http://dx.doi.org/10.1155/2013/601243 |
| spellingShingle | Ying Zhang Huisheng Zhang Guoyan Chen A Note on the Square Roots of a Class of Circulant Matrices Journal of Applied Mathematics |
| title | A Note on the Square Roots of a Class of Circulant Matrices |
| title_full | A Note on the Square Roots of a Class of Circulant Matrices |
| title_fullStr | A Note on the Square Roots of a Class of Circulant Matrices |
| title_full_unstemmed | A Note on the Square Roots of a Class of Circulant Matrices |
| title_short | A Note on the Square Roots of a Class of Circulant Matrices |
| title_sort | note on the square roots of a class of circulant matrices |
| url | http://dx.doi.org/10.1155/2013/601243 |
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