Preconditioning in Expectation
Data Structures and Algorithms
2014-01-27 v1 Numerical Analysis
Numerical Analysis
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 .
Keywords
Cite
@article{arxiv.1401.6236,
title = {Preconditioning in Expectation},
author = {Michael B. Cohen and Rasmus Kyng and Jakub W. Pachocki and Richard Peng and Anup Rao},
journal= {arXiv preprint arXiv:1401.6236},
year = {2014}
}