The Lyapunov exponent and joint spectral radius of pairs of matrices are hard - when not impossible - to compute and to approximate
The authors show that the joint spectral radius and the generalized spectral radius 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. Some applications of these results are discussed.
scientific article; zbMATH DE number 1062600
scientific article