Computing the joint spectral radius Original Research Article

This paper presents algorithms for finding an arbitrarily small interval that contains the joint spectral radius of a finite set of matrices. It also presents a numerical criterion for verifying in certain cases that the joint spectral radius is the maximum of the spectral radii of the given matrices. Error bounds are derived for the case where calculations are done with finite precision and the matrices are not known exactly. The algorithms are implemented and applied to estimate Hölder exponents of the orthonormal wavelets Nphi constructed by Daubechies for 3 less-than-or-equals, slant N less-than-or-equals, slant 8.