Randomized Numerical Linear Algebra: Foundations & Algorithms
Abstract
This survey describes probabilistic algorithms for linear algebra computations, such as factorizing matrices and solving linear systems. It focuses on techniques that have a proven track record for real-world problem instances. The paper treats both the theoretical foundations of the subject and the practical computational issues. Topics covered include norm estimation; matrix approximation by sampling; structured and unstructured random embeddings; linear regression problems; low-rank approximation; subspace iteration and Krylov methods; error estimation and adaptivity; interpolatory and CUR factorizations; Nystr\"om approximation of positive-semidefinite matrices; single view ("streaming") algorithms; full rank-revealing factorizations; solvers for linear systems; and approximation of kernel matrices that arise in machine learning and in scientific computing.
Cite
@article{arxiv.2002.01387,
title = {Randomized Numerical Linear Algebra: Foundations & Algorithms},
author = {Per-Gunnar Martinsson and Joel Tropp},
journal= {arXiv preprint arXiv:2002.01387},
year = {2021}
}