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Randomized numerical linear algebra: Foundations and algorithms

Published online by Cambridge University Press:  30 November 2020

Per-Gunnar Martinsson  and
Joel A. Tropp
Per-Gunnar Martinsson
Affiliation:
Department of Mathematics, University of Texas at Austin Austin, TX 78712, USA E-mail: pgm@oden.utexas.edu
Joel A. Tropp
Affiliation:
Computing & Mathematical Sciences, California Institute of Technology Pasadena, CA 91125, USA E-mail: jtropp@cms.caltech.edu
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Abstract

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.

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Type
Research Article
Information
Acta Numerica , Volume 29 , May 2020 , pp. 403 - 572
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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