The Inverses of Block Toeplitz Matrices
We study the inverses of block Toeplitz matrices based on the analysis of the block cyclic displacement. New formulas for the inverses of block Toeplitz matrices are proposed. We show that the inverses of block Toeplitz matrices can be decomposed as a sum of products of block circulant matrices. In...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/207176 |
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| _version_ | 1832550798787084288 |
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| author | Xiao-Guang Lv Ting-Zhu Huang |
| author_facet | Xiao-Guang Lv Ting-Zhu Huang |
| author_sort | Xiao-Guang Lv |
| collection | DOAJ |
| description | We study the inverses of block Toeplitz matrices based on the analysis of the block cyclic displacement. New formulas for the inverses of block Toeplitz matrices are proposed. We show that the inverses of block Toeplitz matrices can be decomposed as a sum of products of block circulant matrices. In the scalar case, the inverse formulas are proved to be numerically forward stable, if the Toeplitz matrix is nonsingular and well conditioned. |
| format | Article |
| id | doaj-art-ab73a224ed0645f4b1c0ba19c7f54109 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-ab73a224ed0645f4b1c0ba19c7f541092025-02-03T06:05:50ZengWileyJournal of Mathematics2314-46292314-47852013-01-01201310.1155/2013/207176207176The Inverses of Block Toeplitz MatricesXiao-Guang Lv0Ting-Zhu Huang1School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, ChinaSchool of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, ChinaWe study the inverses of block Toeplitz matrices based on the analysis of the block cyclic displacement. New formulas for the inverses of block Toeplitz matrices are proposed. We show that the inverses of block Toeplitz matrices can be decomposed as a sum of products of block circulant matrices. In the scalar case, the inverse formulas are proved to be numerically forward stable, if the Toeplitz matrix is nonsingular and well conditioned.http://dx.doi.org/10.1155/2013/207176 |
| spellingShingle | Xiao-Guang Lv Ting-Zhu Huang The Inverses of Block Toeplitz Matrices Journal of Mathematics |
| title | The Inverses of Block Toeplitz Matrices |
| title_full | The Inverses of Block Toeplitz Matrices |
| title_fullStr | The Inverses of Block Toeplitz Matrices |
| title_full_unstemmed | The Inverses of Block Toeplitz Matrices |
| title_short | The Inverses of Block Toeplitz Matrices |
| title_sort | inverses of block toeplitz matrices |
| url | http://dx.doi.org/10.1155/2013/207176 |
| work_keys_str_mv | AT xiaoguanglv theinversesofblocktoeplitzmatrices AT tingzhuhuang theinversesofblocktoeplitzmatrices AT xiaoguanglv inversesofblocktoeplitzmatrices AT tingzhuhuang inversesofblocktoeplitzmatrices |