On semidefinite programming characterizations of the numerical radius and its dual norm

Autor:	Friedland, Shmuel, Li, Chi-Kwong
Rok vydání:	2023
Předmět:	Mathematics - Numerical Analysis Mathematics - Optimization and Control 15A60 15A69 68Q25 68W25 81P40 90C22 90C51
Druh dokumentu:	Working Paper
Popis:	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 $\varepsilon$ precision are polynomially time computable in the data and $|\log \varepsilon |$ 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 nuclear norm of $2\times n\times m$ real tensor in terms of the numerical radius and its dual norm. Comment: 17 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2308.07287 Zobrazit plný text záznamu View this record from Arxiv