离散非交换饥饿户田网格及其在矩阵计算中的应用

IF 1.7 3区数学 Q2 MATHEMATICS, APPLIED

Numerical Algorithms Pub Date : 2024-08-08 DOI:10.1007/s11075-024-01915-8

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

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引用次数: 0

摘要

在本文中，我们计划利用非交换可积分系统和矩阵值正交多项式的思想，展示一种块海森伯矩阵的特征值算法。我们引入了相邻的矩阵值（theta）变形的双正交多项式族，并从多项式的离散谱变换推导出相应的离散非交换饿户田网格。研究表明，该离散系统可用作块海森伯矩阵的预处理算法。此外，还介绍了该算法的一些收敛分析和数值示例。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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

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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.

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来源期刊

Numerical Algorithms 数学-应用数学

CiteScore

4.00

自引率

9.50%

发文量

201

审稿时长

9 months

期刊介绍： The journal Numerical Algorithms is devoted to numerical algorithms. It publishes original and review papers on all the aspects of numerical algorithms: new algorithms, theoretical results, implementation, numerical stability, complexity, parallel computing, subroutines, and applications. Papers on computer algebra related to obtaining numerical results will also be considered. It is intended to publish only high quality papers containing material not published elsewhere.