Discrete non-commutative hungry Toda lattice and its application in matrix computation
<|reference_start|>Discrete non-commutative hungry Toda lattice and its application in matrix computation: 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.<|reference_end|>
@article{wang2024discrete,
    title={Discrete non-commutative hungry Toda lattice and its application in
  matrix computation},
    author={Zheng Wang, Shi-Hao Li, Kang-Ya Lu and Jian-Qing Sun},
    journal={arXiv preprint arXiv:2404.13492},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.13492},
    primaryClass={math.NA cs.NA math-ph math.MP nlin.SI}
}