تقرير
Discrete non-commutative hungry Toda lattice and its application in matrix computation
| العنوان: | Discrete non-commutative hungry Toda lattice and its application in matrix computation |
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| المؤلفون: | Wang, Zheng, Li, Shi-Hao, Lu, Kang-Ya, Sun, Jian-Qing |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science Mathematics Mathematical Physics Nonlinear Sciences |
| مصطلحات موضوعية: | Mathematics - Numerical Analysis, Mathematical Physics, Nonlinear Sciences - Exactly Solvable and Integrable Systems |
| الوصف: | 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 $\theta$-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. Comment: 24 pages, 2 figures. Comments are welcome |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2404.13492 |
| رقم الأكسشن: | edsarx.2404.13492 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |