Randomized numerical linear algebra: Foundations and algorithms
By Per-Gunnar Martinsson, Joel A. Tropp. Acta Numerica, 2020
522 citations recorded by the source corpus.
This survey describes probabilistic algorithms for linear algebraic computations, such as factorizing matrices and solving linear systems. It focuses on techniques that have a proven track record for real-world problems. The paper treats both the theoretical foundations of the subject and practical computational issues. Topics 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.
Subfields: Artificial Intelligence, Computational Mechanics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/733b412172362627fb6c1d3c24aad500a6f782ec
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In Artificial Intelligence
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- Michael I. Jordan
In Computational Mechanics
In Computational Theory and Mathematics
Citations in the corpus
- Datamodels: Predicting Predictions from Training Data (2022, background): “Note that solving large linear systems efficiently is an area of active research ((Martinsson & Tropp, 2020)), and as a result we anticipate that datamodel estimation could be significantly improved by applying techniques from numerical optimization.”