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

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