An alternative recursive approach to functions of simple triangular matrices
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910485979332608 |
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| author | Baake, Ellen Baake, Michael |
| author_facet | Baake, Ellen Baake, Michael |
| contents | The computation of matrix functions is a well-studied problem. Of special importance are the exponential and the logarithm of a matrix, where the latter also raises existence and uniqueness questions. This is particularly relevant in the context of matrix semigroups and their generators. Here, we look at matrix functions of triangular matrices, where a recursive approach is possible when the matrix has simple spectrum. The special feature is that no knowledge of eigenvectors is required, and that the same recursion applies to the computation of multiple functions or semigroups simultaneously. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_09430 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An alternative recursive approach to functions of simple triangular matrices Baake, Ellen Baake, Michael Rings and Algebras 15A16, 15B51, 60J27 The computation of matrix functions is a well-studied problem. Of special importance are the exponential and the logarithm of a matrix, where the latter also raises existence and uniqueness questions. This is particularly relevant in the context of matrix semigroups and their generators. Here, we look at matrix functions of triangular matrices, where a recursive approach is possible when the matrix has simple spectrum. The special feature is that no knowledge of eigenvectors is required, and that the same recursion applies to the computation of multiple functions or semigroups simultaneously. |
| title | An alternative recursive approach to functions of simple triangular matrices |
| topic | Rings and Algebras 15A16, 15B51, 60J27 |
| url | https://arxiv.org/abs/2406.09430 |