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

Abstract

We give a semidefinite programming characterizations of the numerical radius and its dual norm for quaternionic matrices. We show that the computation of the numerical radius and its dual norm within $\epsilon$ precision are polynomially time computable in the data and $|\log \epsilon |$ using the short step, primal interior point method.

arXiv comment23 pages. To appear in Communications in Optimization Theory