Ultradiscrete hungry Toda equation and eigenvalues over min-plus algebra

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-11-03 DOI:10.1080/10236198.2023.2277714

Masafumi Kan, Akiko Fukuda, Sennosuke Watanabe

引用次数: 0

Abstract

The recursion formula of the quotient difference algorithm for computing matrix eigenvalues corresponds with the discrete Toda equation, which is well-known in discrete integrable systems. Previous studies have revealed that the ultradiscrete Toda equation computes eigenvalues of tridiagonal matrices over the min-plus algebra. The min-plus algebra is a commutative semiring in which minimum and plus operations are introduced into the union of the set of real numbers and positive infinity. The discrete hungry Toda equation, which is a generalization of the discrete Toda equation, can compute the eigenvalues of lower Hessenberg banded matrices. This study focuses on the ultradiscrete hungry Toda equation and show that the time evolution of the equation yields the eigenvalues of lower Hessenberg banded matrices over the min-plus algebra.

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超离散饥饿Toda方程和特征值在最小加代数

计算矩阵特征值的商差分算法的递推公式对应于离散可积系统中众所周知的离散Toda方程。以往的研究表明，超离散Toda方程可以计算min +代数上的三对角矩阵的特征值。最小加代数是一个交换半环，在这个半环中，在实数集与正无穷的并集中引入了最小和加运算。离散饥饿Toda方程是对离散Toda方程的推广，它可以计算下Hessenberg带状矩阵的特征值。本文研究了超离散饥饿Toda方程，并证明了该方程的时间演化产生了下Hessenberg带状矩阵在min-plus代数上的特征值。

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.