An experimental comparison of methods for computing the numerical radius

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.

Keywords

• Semidefinite programming
• Convex optimization
• Nonconvex optimization
• Field of values
• Numerical range