论数值半径及其双规范的半有限编程特征

IF 1.5 2区数学 Q2 MATHEMATICS, APPLIED SIAM Journal on Matrix Analysis and Applications Pub Date : 2024-07-23 DOI:10.1137/23m160356x

Shmuel Friedland, Chi-Kwong Li

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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 3 期，第 1414-1428 页，2024 年 9 月。摘要。我们陈述并给出了矩阵数值半径及其对偶法的半有限编程特征的自足证明。我们证明，在[math]精度范围内计算数值半径及其对偶法，在数据和[math]中使用椭球法或短步原始内点法都是多项式时间可计算的。我们应用我们的结果给出了一个简单的公式，用数值半径及其对偶法计算[数学]实张量的谱法和核规范。

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On Semidefinite Programming Characterizations of the Numerical Radius and Its Dual Norm

SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 3, Page 1414-1428, September 2024.
Abstract. We state and give self-contained proofs of semidefinite programming characterizations of the numerical radius and its dual norm for matrices. We show that the computation of the numerical radius and its dual norm within [math] precision are polynomially time computable in the data and [math] using either the ellipsoid method or the short step, primal interior point method. We apply our results to give a simple formula for the spectral and the nuclear norm of a [math] real tensor in terms of the numerical radius and its dual norm.

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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.