Discrete non-commutative hungry Toda lattice and its application in matrix computation
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913323144970240 |
|---|---|
| author | Wang, Zheng Li, Shi-Hao Lu, Kang-Ya Sun, Jian-Qing |
| author_facet | Wang, Zheng Li, Shi-Hao Lu, Kang-Ya Sun, Jian-Qing |
| contents | In this paper, we plan to show an eigenvalue algorithm for block Hessenberg matrices by using the idea of non-commutative integrable systems and matrix-valued orthogonal polynomials. We introduce adjacent families of matrix-valued $θ$-deformed bi-orthogonal polynomials, and derive corresponding discrete non-commutative hungry Toda lattice from discrete spectral transformations for polynomials. It is shown that this discrete system can be used as a pre-precessing algorithm for block Hessenberg matrices. Besides, some convergence analysis and numerical examples of this algorithm are presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_13492 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Discrete non-commutative hungry Toda lattice and its application in matrix computation Wang, Zheng Li, Shi-Hao Lu, Kang-Ya Sun, Jian-Qing Numerical Analysis Mathematical Physics Exactly Solvable and Integrable Systems In this paper, we plan to show an eigenvalue algorithm for block Hessenberg matrices by using the idea of non-commutative integrable systems and matrix-valued orthogonal polynomials. We introduce adjacent families of matrix-valued $θ$-deformed bi-orthogonal polynomials, and derive corresponding discrete non-commutative hungry Toda lattice from discrete spectral transformations for polynomials. It is shown that this discrete system can be used as a pre-precessing algorithm for block Hessenberg matrices. Besides, some convergence analysis and numerical examples of this algorithm are presented. |
| title | Discrete non-commutative hungry Toda lattice and its application in matrix computation |
| topic | Numerical Analysis Mathematical Physics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2404.13492 |