Work

A Sketch-and-Select Arnoldi Process

Year: 2024

Type: article

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]). [Formula: see text]

Source: SIAM Journal on Scientific Computing

DOI: 10.1137/23m1588007

Authors: Stefan Güttel, Igor Simunec

Institutions: University of Manchester, Scuola Normale Superiore

Language: English

Topic: Matrix Theory and Algorithms

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: Alan Turing Institute, Royal Society, Engineering and Physical Sciences Research Council

Awards: G44814566, The Alan Turing Institute 20/21 - 21/22, G6166080336