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

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 $\mathrm{\mid }\log \epsilon \mathrm{\mid }$ using the short step, primal interior point method.