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

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-08-08 DOI:10.1007/s11075-024-01915-8

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

引用次数: 0

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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离散非交换饥饿户田网格及其在矩阵计算中的应用

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。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.