Randomized Numerical Linear Algebra: Foundations & Algorithms
Per‐Gunnar Martinsson, Joel A. Tropp · arXiv (Cornell University) · 2020
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; Nyström 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.