Dissecting the FEAST algorithm for generalized eigenproblems

We analyze the FEAST method for computing selected eigenvalues and eigenvectors of large sparse matrix pencils. After establishing the close connection between FEAST and the well-known Rayleigh–Ritz method, we identify several critical issues that influence convergence and accuracy of the solver: th...

Full description

Saved in:
Bibliographic Details
Published in:Journal of computational and applied mathematics 2013-05, Vol.244, p.1-9
Main Authors: Krämer, Lukas, Di Napoli, Edoardo, Galgon, Martin, Lang, Bruno, Bientinesi, Paolo
Format: Article
Language:English
Subjects:
Complement
Computation
Contour integration
Convergence
Eigenvalues
FEAST algorithm
Generalized eigenvalue problem
Linear systems
Mathematical analysis
Mathematical models
Rayleigh–Ritz method
Solvers
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We analyze the FEAST method for computing selected eigenvalues and eigenvectors of large sparse matrix pencils. After establishing the close connection between FEAST and the well-known Rayleigh–Ritz method, we identify several critical issues that influence convergence and accuracy of the solver: the choice of the starting vector space, the stopping criterion, how the inner linear systems impact the quality of the solution, and the use of FEAST for computing eigenpairs from multiple intervals. We complement the study with numerical examples, and hint at possible improvements to overcome the existing problems.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2012.11.014