2023/08/04 by Liam Burke, Stefan Güttel, Burke, Liam +1
Computer Science · Physics and Astronomy · #65F10 #65F50 #65F60 #68W20 #Electromagnetic Scattering and Analysis #FOS: Mathematics #Matrix Theory and Algorithms #Model Reduction and Neural Networks #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2308.02290
openalex publication_date 2023/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.