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A Krylov subspace recycling method for the efficient evaluation of a sequenceof matrix functions acting on a set of vectors is developed. The methodimproves over the recycling methods presented in [Burke et al.,arXiv:2209.14163, 2022] in that it uses a closed-form expression for theaugmented FOM approximants and hence circumvents the use of numericalquadrature. We further extend our method to use randomized sketching in orderto avoid the arithmetic cost of orthogonalizing a full Krylov basis, offeringan attractive solution to the fact that recycling algorithms built from shiftedaugmented FOM cannot easily be restarted. The efficacy of the proposedalgorithms is demonstrated with numerical experiments.

Krylov Subspace Recycling With Randomized Sketching For Matrix Functions