频谱最大化产品并非一般独一无二

IF 1.5 2区数学 Q2 MATHEMATICS, APPLIED

SIAM Journal on Matrix Analysis and Applications Pub Date : 2024-02-08 DOI:10.1137/23m1550621

Jairo Bochi, Piotr Laskawiec

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引用次数: 0

摘要

SIAM 矩阵分析与应用期刊》，第 45 卷，第 1 期，第 585-600 页，2024 年 3 月。摘要。人们普遍认为，[数学]矩阵的典型有限族允许达到联合谱半径的有限乘积。这一猜想得到了计算实验的支持，并自然而然地引出了下面的问题：这些频谱最大化乘积是否通常是唯一的，直至循环排列和幂级数？我们的回答是否定的。正如霍洛维茨（Horowitz）在五十年前发现的那样，有一些矩阵的乘积尽管不是彼此的循环排列，却总是具有相同的频谱半径。我们证明，最简单的霍洛维茨乘积也能以稳健的方式实现频谱最大化；更确切地说，我们展示了[math]矩阵[math]对的一个小而非空的开放子集，对于这个子集，[math]和[math]乘积都能实现频谱最大化。

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Spectrum Maximizing Products Are Not Generically Unique

SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 585-600, March 2024.
Abstract. It is widely believed that typical finite families of [math] matrices admit finite products that attain the joint spectral radius. This conjecture is supported by computational experiments and it naturally leads to the following question: are these spectrum maximizing products typically unique, up to cyclic permutations and powers? We answer this question negatively. As discovered by Horowitz around fifty years ago, there are products of matrices that always have the same spectral radius despite not being cyclic permutations of one another. We show that the simplest Horowitz products can be spectrum maximizing in a robust way; more precisely, we exhibit a small but nonempty open subset of pairs of [math] matrices [math] for which the products [math] and [math] are both spectrum maximizing.

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来源期刊

SIAM Journal on Matrix Analysis and Applications 数学-应用数学

CiteScore

2.90

自引率

6.70%

发文量

审稿时长

6-12 weeks

期刊介绍： The SIAM Journal on Matrix Analysis and Applications contains research articles in matrix analysis and its applications and papers of interest to the numerical linear algebra community. Applications include such areas as signal processing, systems and control theory, statistics, Markov chains, and mathematical biology. Also contains papers that are of a theoretical nature but have a possible impact on applications.