Computation of quasiseparable representations of Green matrices
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | |
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| _version_ | 1866918183957430272 |
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| author | Boito, Paola Eidelman, Yuli |
| author_facet | Boito, Paola Eidelman, Yuli |
| contents | The well-known Asplund theorem states that the inverse of a (possibly one-sided) band matrix $A$ is a Green matrix. In accordance with quasiseparable theory, such a matrix admits a quasiseparable representation in its rank-structured part. Based on this idea, we derive algorithms that compute a quasiseparable representation of $A^{-1}$ with linear complexity. Many inversion algorithms for band matrices exist in the literature. However, algorithms based on a computation of the rank structure performed theoretically via the Asplund theorem appear for the first time in this paper. Numerical experiments confirm complexity estimates and offer insight into stability properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_02701 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Computation of quasiseparable representations of Green matrices Boito, Paola Eidelman, Yuli Numerical Analysis The well-known Asplund theorem states that the inverse of a (possibly one-sided) band matrix $A$ is a Green matrix. In accordance with quasiseparable theory, such a matrix admits a quasiseparable representation in its rank-structured part. Based on this idea, we derive algorithms that compute a quasiseparable representation of $A^{-1}$ with linear complexity. Many inversion algorithms for band matrices exist in the literature. However, algorithms based on a computation of the rank structure performed theoretically via the Asplund theorem appear for the first time in this paper. Numerical experiments confirm complexity estimates and offer insight into stability properties. |
| title | Computation of quasiseparable representations of Green matrices |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2308.02701 |