English

A Note on Preconditioning by Low-Stretch Spanning Trees

Numerical Analysis 2009-03-17 v1 Data Structures and Algorithms

Abstract

Boman and Hendrickson observed that one can solve linear systems in Laplacian matrices in time \bigOm3/2+o(1)ln(1/ϵ)\bigO{m^{3/2 + o (1)} \ln (1/\epsilon)} by preconditioning with the Laplacian of a low-stretch spanning tree. By examining the distribution of eigenvalues of the preconditioned linear system, we prove that the preconditioned conjugate gradient will actually solve the linear system in time \softOm4/3ln(1/ϵ)\softO{m^{4/3} \ln (1/\epsilon)}.

Cite

@article{arxiv.0903.2816,
  title  = {A Note on Preconditioning by Low-Stretch Spanning Trees},
  author = {Daniel A Spielman and Jaeoh Woo},
  journal= {arXiv preprint arXiv:0903.2816},
  year   = {2009}
}
R2 v1 2026-06-21T12:41:11.559Z