Krylov Subspace Restarting for Matrix Laplace Transforms
Andreas Frommer, Karsten Kahl, M. Schweitzer, Manuel Tsolakis · SIAM Journal on Matrix Analysis and Applications · 2023
Abstract. A common way to approximate [Formula: see text]—the action of a matrix function on a vector—is to use the Arnoldi approximation. Since a new vector needs to be generated and stored in every iteration, one is often forced to rely on restart algorithms which are either not efficient, not stable, or applicable only to restricted classes of functions. We present a new representation of the error of the Arnoldi iterates if the function [Formula: see text] is given as a Laplace transform. Based on this representation we build an efficient and stable restart algorithm. In doing so we extend earlier work for the class of Stieltjes functions which are special Laplace transforms. We report several numerical experiments including comparisons with the restart method for Stieltjes functions.