A Note on Preconditioning by Low-Stretch Spanning Trees

Details A Note on Preconditioning by Low-Stretch Spanning Trees A Note on Preconditioning by Low-Stretch Spanning Trees

2009-03-16

arxiv.org/abs/0903.2816v1

Computer Science

Numerical Analysis

Scientific paper

Boman and Hendrickson observed that one can solve linear systems in Laplacian matrices in time $\bigO{m^{3/2 + o (1)} \ln (1/\epsilon)}$ 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 $\softO{m^{4/3} \ln (1/\epsilon)}$.

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