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Discrete non-commutative hungry Toda lattice and its application in matrix computation
- Publication Year :
- 2024
-
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.<br />Comment: 24 pages, 2 figures. Comments are welcome
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2404.13492
- Document Type :
- Working Paper