Tridiagonal and single-pair matrices and the inverse sum of two single-pair matrices
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866916141807435776 |
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| author | Bossu, Sebastien |
| author_facet | Bossu, Sebastien |
| contents | A novel factorization for the sum of two single-pair matrices is established as product of lower-triangular, tridiagonal, and upper-triangular matrices, leading to semi-closed-form formulas for tridiagonal matrix inversion. Subsequent factorizations are established, leading to semi-closed-form formulas for the inverse sum of two single-pair matrices. An application to derive the symbolic inverse of a particular Gram matrix is presented, and the numerical stability of the formulas is studied. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_06100 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Tridiagonal and single-pair matrices and the inverse sum of two single-pair matrices Bossu, Sebastien Rings and Algebras 15B99, 15B05, 47B36, 15-04 A novel factorization for the sum of two single-pair matrices is established as product of lower-triangular, tridiagonal, and upper-triangular matrices, leading to semi-closed-form formulas for tridiagonal matrix inversion. Subsequent factorizations are established, leading to semi-closed-form formulas for the inverse sum of two single-pair matrices. An application to derive the symbolic inverse of a particular Gram matrix is presented, and the numerical stability of the formulas is studied. |
| title | Tridiagonal and single-pair matrices and the inverse sum of two single-pair matrices |
| topic | Rings and Algebras 15B99, 15B05, 47B36, 15-04 |
| url | https://arxiv.org/abs/2304.06100 |