QUT ePrints

Krylov subspaces and the analytic grade

Ilic, Milos & Turner, Ian W. (2005) Krylov subspaces and the analytic grade. Numerical Linear Algebra with Applications, 12(1), pp. 55-76.

View at publisher

Abstract

Typical behaviour of the solution of a linear system of equations obtained iteratively by Krylov methods can be characterized by three stages. Initially the residual diminishes steadily; this is followed by stagnation and finally rapid convergence near the algebraic grade. This study examines this behaviour in terms of the concepts of approximately invariant subspace and what we have called the analytic grade of a Krylov sequence. It is shown how the small Ritz values play a vital role in the convergence and how this knowledge helps in the construction of an effective preconditioner.

Impact and interest:

6 citations in Scopus
Search Google Scholar™
4 citations in Web of Science®

Citation countsare sourced monthly from Scopus and Web of Science® citation databases.

These databases contain citations from different subsets of available publications and different time periods and thus the citation count from each is usually different. Some works are not in either database and no count is displayed. Scopus includes citations from articles published in 1996 onwards, and Web of Science® generally from 1980 onwards.

Citations counts from the Google Scholar™ indexing service can be viewed at the linked Google Scholar™ search.

ID Code: 8190
Item Type: Journal Article
Additional Information: For more information, please refer to the journal's website (see hypertext link) or contact the author. Author contact details: i.turner@qut.edu.au
Keywords: preconditioning, approximately invariant subspaces, convergence, error bounds, Ritz values
DOI: 10.1002/nla.392
ISSN: 1070-5325
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300) > Numerical Analysis (010301)
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Copyright Owner: Copyright 2005 John Wiley & Sons
Deposited On: 22 Jun 2007
Last Modified: 29 Feb 2012 23:07

Export: EndNote | Dublin Core | BibTeX

Repository Staff Only: item control page