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arXiv · 2404.13492

Discrete non-commutative hungry Toda lattice and its application in matrix computation

Zheng Wang·Shi-Hao Li·Kang-Ya Lu·Jian-Qing Sun
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Abstract

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.

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Zheng Wang, Shi-Hao Li, Kang-Ya Lu, Jian-Qing Sun. 2024-04-21. Discrete non-commutative hungry Toda lattice and its application in matrix computation. https://arxiv.org/abs/2404.13492

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