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arXiv · 1609.00048

Practical sketching algorithms for low-rank matrix approximation

Joel A. Tropp·Alp Yurtsever·Madeleine Udell·Volkan Cevher
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Abstract

This paper describes a suite of algorithms for constructing low-rank approximations of an input matrix from a random linear image of the matrix, called a sketch. These methods can preserve structural properties of the input matrix, such as positive-semidefiniteness, and they can produce approximations with a user-specified rank. The algorithms are simple, accurate, numerically stable, and provably correct. Moreover, each method is accompanied by an informative error bound that allows users to select parameters a priori to achieve a given approximation quality. These claims are supported by numerical experiments with real and synthetic data.

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Joel A. Tropp, Alp Yurtsever, Madeleine Udell, Volkan Cevher. 2018-01-02. Practical sketching algorithms for low-rank matrix approximation. https://doi.org/10.1137/17m1111590

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