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Randomized Numerical Linear Algebra: Foundations & Algorithms

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arxiv 2002.01387 v3 pith:DAUOXDQP submitted 2020-02-04 math.NA cs.NA

Per-Gunnar Martinsson , Joel Tropp This is my paper · ORCID
classification math.NAcs.NA
keywords linearapproximationalgorithmsmatricesalgebraestimationfactorizationsfoundations
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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.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. High-dimensional reliability-oriented Shapley effect estimation with Normalizing Flows

    stat.ME 2026-06 unverdicted novelty 6.5 of 10

    Target Shapley effects for high-dimensional correlated reliability problems can be estimated from a single failing sample by rewriting closed target Sobol indices via conditional densities and fitting those densities ...

  2. Estimating eigenvectors and eigenspaces of covariance matrices: Optimal Bounds and Conditions for Consistency

    math.ST 2026-07 conditional novelty 6.0 of 10

    Sample-covariance eigenvector and eigenspace errors are determined up to constant factors by the effective rank and the signal-to-gap ratio, giving near-optimal consistency thresholds.

  3. Sequential Least-Squares Estimators with Fast Randomized Sketching for Linear Statistical Models

    stat.ML 2025-09 conditional novelty 5.0 of 10

    SLSE-FRS solves least squares through increasingly larger random sketches, reaching exact least-squares accuracy at roughly linear cost.

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