Krylov subspaces and the analytic grade
(2005) Krylov subspaces and the analytic grade. Numerical Linear Algebra with Applications 12(1):pp. 55-76.
Full text available as: |
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.
| Item Type: | Journal Article |
|---|---|
| RM Number: | 2005000991 |
| Status: | Published |
| Keywords: | preconditioning; approximately invariant subspaces; convergence; error bounds; Ritz values |
| Subjects: | 230000 Mathematical Sciences > 230100 Mathematics > 230116 Numerical Analysis |
| ID Code: | 8190 |
| Deposited By: | Conlon, Kylie |
| Deposited On: | 22 June 2007 |
| Alternative Locations: | http://dx.doi.org/10.1002/nla.392 |
| Copyright Owner: | Copyright 2005 John Wiley & Sons |
| 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 |