English

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 mlog1/2nm\log^{1/2}n .

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}
}
R2 v1 2026-06-22T02:53:51.338Z