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A common way to approximate $F(A)b$ -- the action of a matrix function on avector -- is to use the Arnoldi approximation. Since a new vector needs to begenerated and stored in every iteration, one is often forced to rely on restartalgorithms which are either not efficient, not stable or only applicable torestricted classes of functions. We present a new representation of the errorof the Arnoldi iterates if the function $F$ is given as a Laplace transform.Based on this representation we build an efficient and stable restartalgorithm. In doing so we extend earlier work for the class of Stieltjesfunctions which are special Laplace transforms. We report several numericalexperiments including comparisons with the restart method for Stieltjesfunctions.

Krylov subspace restarting for matrix Laplace transforms