A Sketch-and-Select Arnoldi Process

Abstract

SIAM Journal on Scientific Computing, Volume 46, Issue 4, Page A2774-A2797, August 2024.
Abstract. A sketch-and-select Arnoldi process to generate a well-conditioned basis of a Krylov space at low cost is proposed. At each iteration the procedure utilizes randomized sketching to select a limited number of previously computed basis vectors to project out of the current basis vector. The computational cost grows linearly with the dimension of the Krylov space. The subset selection problem for the projection step is approximately solved with a number of heuristic algorithms and greedy methods used in statistical learning and compressive sensing. Reproducibility of computational results. This paper has been awarded the “SIAM Reproducibility Badge: Code and data available” as a recognition that the authors have followed reproducibility principles valued by SISC and the scientific computing community. Code and data that allow readers to reproduce the results in this paper are available at https://github.com/simunec/sketch-select-arnoldi and in the supplementary materials (sketch-select-arnoldi-main.zip [2.21MB]).