A Low-Rank Approximation for Computing the Matrix Exponential Norm
Yu. M. Nechepurenko, Miloud Sadkane · SIAM Journal on Matrix Analysis and Applications · 2011
This work is devoted to computing the function [Formula: see text] in a given time interval [Formula: see text], where [Formula: see text] is a square matrix whose eigenvalues have negative real parts. The main emphasis is put on computations of the maximal value of [Formula: see text] for [Formula: see text]. 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 [Formula: see text] with a given accuracy. We discuss its implementation and demonstrate its efficiency with some numerical experiments.