We give a semidefinite programming characterization of the dual norm of numerical radius for matrices. This characterization yields a new proof of semidefinite characterization of the numerical radius for matrices, which follows from Ando's characterization. We show that the computation of the numerical radius and its dual norm within $\varepsilon$ precision are polynomially time computable in the data and $|\log \varepsilon |$ using the short step, primal interior point method.

翻译：我们给出了矩阵数值半径对偶半正定规划刻画。这一刻画为矩阵数值半径的半正定规划表征提供了新的证明，该证明源自Ando的刻画。我们证明，利用短步原始内点法，在数据规模和$|\log \varepsilon |$的多项式时间内，可计算$\varepsilon$精度内的数值半径及其对偶范数。