Spectral quantities associated to pairs of matrices are hard, when not impossible, to compute and to approximate
John N. Tsitsiklis, Vincent D. Blondel, Decision Systems. · 1996
We analyse the computability and the complexity of various definitions of spectral radii for sets of matrices. We show that the joint and generalized spectral radii of two integer matrices are not approximable in polynomial time, and that two related quantities -- the lower spectral radius and the largest Lyapunov exponent -- are not algorithmically approximable.