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A sublinear-time randomized algorithm for column and row subset selection based on strong rank-revealing QR factorizations

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arxiv 2402.13975 v1 pith:35NHARPY submitted 2024-02-21 math.NA cs.NA

Alice Cortinovis , Lexing Ying This is my paper · ORCID
classification math.NAcs.NA
keywords algorithmapproximationlow-rankmatrixcolumnserrorrank-revealingrows
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In this work, we analyze a sublinear-time algorithm for selecting a few rows and columns of a matrix for low-rank approximation purposes. The algorithm is based on an initial uniformly random selection of rows and columns, followed by a refinement of this choice using a strong rank-revealing QR factorization. We prove bounds on the error of the corresponding low-rank approximation (more precisely, the CUR approximation error) when the matrix is a perturbation of a low-rank matrix that can be factorized into the product of matrices with suitable incoherence and/or sparsity assumptions.

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Cited by 1 Pith paper

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

  1. A Semi-Lagrangian Adaptive-Rank (SLAR) Method for Linear Advection and Nonlinear Vlasov-Poisson System

    math.NA 2024-11 conditional novelty 6.0 of 10

    A non-splitting semi-Lagrangian adaptive-rank scheme using CUR sampling and SVD truncation is validated for linear advection and 1D1V Vlasov-Poisson equations.

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