Numerical bounds on the Crouzeix ratio for a class of matrices

IF 1.4 2区数学 Q1 MATHEMATICS

Calcolo Pub Date : 2024-06-08 DOI:10.1007/s10092-024-00580-6

Michel Crouzeix, Anne Greenbaum, Kenan Li

引用次数: 0

Abstract

We provide numerical bounds on the Crouzeix ratio for KMS matrices A which have a line segment on the boundary of the numerical range. The Crouzeix ratio is the supremum over all polynomials p of the spectral norm of p(A) divided by the maximum absolute value of p on the numerical range of A. Our bounds satisfy the conjecture that this ratio is less than or equal to 2. We also give a precise description of these numerical ranges.

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一类矩阵的 Crouzeix 比率数值界限

我们提供了 KMS 矩阵 A 的 Crouzeix 比率的数值边界，该矩阵的数值范围边界上有一条线段。Crouzeix 比率是 p(A) 的谱规范的所有多项式 p 的上位数除以 p 在 A 的数值范围上的最大绝对值。我们的界限满足了这一比率小于或等于 2 的猜想。

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

Calcolo 数学-数学

CiteScore

2.40

自引率

11.80%

发文量

审稿时长

>12 weeks

期刊介绍： Calcolo is a quarterly of the Italian National Research Council, under the direction of the Institute for Informatics and Telematics in Pisa. Calcolo publishes original contributions in English on Numerical Analysis and its Applications, and on the Theory of Computation. The main focus of the journal is on Numerical Linear Algebra, Approximation Theory and its Applications, Numerical Solution of Differential and Integral Equations, Computational Complexity, Algorithmics, Mathematical Aspects of Computer Science, Optimization Theory. Expository papers will also appear from time to time as an introduction to emerging topics in one of the above mentioned fields. There will be a "Report" section, with abstracts of PhD Theses, news and reports from conferences and book reviews. All submissions will be carefully refereed.