2.3NAMar 16, 2009
A Note on Preconditioning by Low-Stretch Spanning TreesDaniel A Spielman, Jaeoh Woo
Boman and Hendrickson observed that one can solve linear systems in Laplacian matrices in time $\bigO{m^{3/2 + o (1)} \ln (1/ε)}$ 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 $\softO{m^{4/3} \ln (1/ε)}$.