Graph theoretic proofs for some results on banded inverses of $M$-matrices
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915078736969728 |
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| author | Pratihar, S. Sivakumar, K. C. |
| author_facet | Pratihar, S. Sivakumar, K. C. |
| contents | This work concerns results on conditions guaranteeing that certain banded $M$-matrices have banded inverses. As a first goal, a graph theoretic characterization for an off-diagonal entry of the inverse of an $M$-matrix to be positive, is presented. This result, in turn, is used in providing alternative graph theoretic proofs of the following: (1) a characterization for a tridiagonal $M$-matrix to have a tridiagonal inverse. (2) a necessary condition for an $M$-matrix to have a pentadiagonal inverse. The results are illustrated by several numerical examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_18611 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Graph theoretic proofs for some results on banded inverses of $M$-matrices Pratihar, S. Sivakumar, K. C. General Mathematics 05C50, 05C20, 15A09, 15B48 This work concerns results on conditions guaranteeing that certain banded $M$-matrices have banded inverses. As a first goal, a graph theoretic characterization for an off-diagonal entry of the inverse of an $M$-matrix to be positive, is presented. This result, in turn, is used in providing alternative graph theoretic proofs of the following: (1) a characterization for a tridiagonal $M$-matrix to have a tridiagonal inverse. (2) a necessary condition for an $M$-matrix to have a pentadiagonal inverse. The results are illustrated by several numerical examples. |
| title | Graph theoretic proofs for some results on banded inverses of $M$-matrices |
| topic | General Mathematics 05C50, 05C20, 15A09, 15B48 |
| url | https://arxiv.org/abs/2412.18611 |