On alternating maximization algorithm for computing the hump of matrix powers

Alternating maximization type algorithms for computing the maximal growth of the norm of matrix powers are discussed. Their convergence properties are established under the natural assumption that the matrix is discrete-stable. The implementation considers both the small and large problem sizes, where for the latter case, a variant of the Lanczos method is especially devised. The numerical tests confirm that the main advantages of the alternating maximization technique are its accuracy and speed of convergence.