A Low-Rank Approximation for Computing the Matrix Exponential Norm

This work is devoted to computing the function in a given time interval , where is a square matrix whose eigenvalues have negative real parts. The main emphasis is put on computations of the maximal value of for . To speed up the computations, we propose and justify a new algorithm based on low-rank approximations of the matrix exponential and prove that it computes with a given accuracy. We discuss its implementation and demonstrate its efficiency with some numerical experiments.