Return to search

The Anderson Model of Localization: A Challenge for Modern Eigenvalue Methods

We present a comparative study of the application of modern eigenvalue algorithms to an eigenvalue problem arising in quantum physics, namely, the computation of a few interior eigenvalues and their associated eigenvectors for the large, sparse, real, symmetric, and indefinite matrices of the Anderson model of localization. We compare the Lanczos algorithm in the 1987 implementation of Cullum and Willoughby with the implicitly restarted Arnoldi method coupled with polynomial and several shift-and-invert convergence accelerators as well as with a sparse hybrid tridiagonalization method. We demonstrate that for our problem the Lanczos implementation is faster and more memory efficient than the other approaches. This seemingly innocuous problem presents a major challenge for all modern eigenvalue algorithms.

Identiferoai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:18355
Date09 September 2005
CreatorsElsner, Ulrich, Mehrmann, Volker, Römer, Rudolf A., Schreiber, Michael
PublisherTechnische Universität Chemnitz
Source SetsHochschulschriftenserver (HSSS) der SLUB Dresden
LanguageEnglish
Detected LanguageEnglish
Typedoc-type:preprint, info:eu-repo/semantics/preprint, doc-type:Text
SourcePreprintreihe des Chemnitzer SFB 393
Rightsinfo:eu-repo/semantics/openAccess

Page generated in 0.0017 seconds