An experimental comparison of methods for computing the numerical radius

Tim Mitchell; Michael L. Overton

doi:10.1016/j.rinam.2024.100434

An experimental comparison of methods for computing the numerical radius

Research output: Contribution to journal › Article › peer-review

Abstract

We make an experimental comparison of methods for computing the numerical radius of an n×n complex matrix, based on two well-known characterizations, the first a nonconvex optimization problem in one real variable and the second a convex optimization problem in n²+1 real variables. We make comparisons with respect to both accuracy and computation time using publicly available software.

Original language	English (US)
Article number	100434
Journal	Results in Applied Mathematics
Volume	21
DOIs	https://doi.org/10.1016/j.rinam.2024.100434
State	Published - Feb 2024

Keywords

Convex optimization
Field of values
Nonconvex optimization
Numerical range
Semidefinite programming

ASJC Scopus subject areas

Applied Mathematics

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10.1016/j.rinam.2024.100434

Cite this

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abstract = "We make an experimental comparison of methods for computing the numerical radius of an n×n complex matrix, based on two well-known characterizations, the first a nonconvex optimization problem in one real variable and the second a convex optimization problem in n2+1 real variables. We make comparisons with respect to both accuracy and computation time using publicly available software.",

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AB - We make an experimental comparison of methods for computing the numerical radius of an n×n complex matrix, based on two well-known characterizations, the first a nonconvex optimization problem in one real variable and the second a convex optimization problem in n2+1 real variables. We make comparisons with respect to both accuracy and computation time using publicly available software.

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KW - Semidefinite programming

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An experimental comparison of methods for computing the numerical radius

Abstract

Keywords

ASJC Scopus subject areas

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