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arXiv · 1401.6236

Preconditioning in Expectation

Michael B. Cohen·Rasmus Kyng·Jakub W. Pachocki·Richard Peng·Anup Rao
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Abstract

We show that preconditioners constructed by random sampling can perform well without meeting the standard requirements of iterative methods. When applied to graph Laplacians, this leads to ultra-sparsifiers that in expectation behave as the nearly-optimal ones given by [Kolla-Makarychev-Saberi-Teng STOC`10]. Combining this with the recursive preconditioning framework by [Spielman-Teng STOC`04] and improved embedding algorithms, this leads to algorithms that solve symmetric diagonally dominant linear systems and electrical flow problems in expected time close to $m\log^{1/2}n$ .

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Michael B. Cohen, Rasmus Kyng, Jakub W. Pachocki, Richard Peng, Anup Rao. 2014-01-24. Preconditioning in Expectation. https://arxiv.org/abs/1401.6236

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