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：本文给出了矩阵数值半径对偶范数的半正定规划特征刻画。该刻画为矩阵数值半径的半正定特征提供了新的证明，这一结果源自Ando的经典特征。我们证明，利用短步原始内点法，在$\varepsilon$精度下计算数值半径及其对偶范数在数据规模和$|\log \varepsilon |$范围内是多项式时间可计算的。