A Krylov subspace recycling method for the efficient evaluation of a sequence
of matrix functions acting on a set of vectors is developed. The method
improves over the recycling methods presented in [Burke et al.,
arXiv:2209.14163, 2022] in that it uses a closed-form expression for the
augmented FOM approximants and hence circumvents the use of numerical
quadrature. We further extend our method to use randomized sketching in order
to avoid the arithmetic cost of orthogonalizing a full Krylov basis, offering
an attractive solution to the fact that recycling algorithms built from shifted
augmented FOM cannot easily be restarted. The efficacy of the proposed
algorithms is demonstrated with numerical experiments.Comment: 19 pages, 5 figure