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 $n\times n$ 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 $n^{2}+1$ real variables. We make comparisons with respect to both accuracy and computation time using publicly available software.