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Two useful measures of the robust stability of the discrete-time dynamical system x k+1 = Ax k are the -pseudospectral radius and the numerical radius of A. The -pseudospectral radius of A is the largest of the moduli of the points in the -pseudospectrum of A, while the numerical radius is the largest of the moduli of the points in the field of values. We present globally convergent algorithms for computing the -pseudospectral radius and the numerical radius. For the former algorithm, wedoi:10.1093/imanum/dri012 fatcat:bnyvlkgrmna55h7w6jwo7tihiy