From: polman@sci.kun.nl (Ben Polman) Subject: Re: Eigenvalues for sparse Matrices Date: 8 Jun 1999 12:20:19 +0200 Newsgroups: sci.math.num-analysis Keywords: Largest eigenvalues with Arnoldi, Davidson methods In shepard@tcg.anl.gov (Ron Shepard) writes: >In article <7jg5th$b7m$1@sun27.hrz.tu-darmstadt.de>, >spellucci@mathematik.tu-darmstadt.de (Peter Spellucci) wrote: >>In article <375A8615.167E@ica1.uni-stuttgart.de>, >> Hans-Georg Matuttis writes: >>|> I have the following question on eigenvalues for (large) >>|> sparse Matrices: >>|> - Is there something better than thes Lanczos-Algorithm >>|> for computing the largest eigenvalue of a large sparse >>|> Matrix? Literature would be appreciated ..... >>parlett: the symmetric eigenvalue problem. >> (republished by SIAM) >>Lanczos is an optimal method for the symmetric case. >>for the nonsymmetric case the arnoldi-method is the >>aequivalent >In my field of computational chemistry, the Davidson method is used most >often when only a few eigenpairs are needed. The convergence is always >faster than Lanczos, but you have a dense subspace representation rather >than the tridiagonal one. There has been some recent analysis by a Dutch >group (I forget the name) that shows how to accelerate convergence with >only a slight increase in computational effort. van der Vorst and Sleijpen on the Jacobi-Davidsom method see http://www.math.uu.nl/people/sleijpen/ best regards, Ben -- --------------------------------------------------------------------- Dr. B.J.W. Polman, Department of Mathematics, University of Nijmegen. Toernooiveld, 6525 ED Nijmegen, The Netherlands, Phone: +31-24-3652862 e-mail: polman@sci.kun.nl