On Linear Least-Squares Problems with Diagonally Dominant Weight Matrices
The solution of the unconstrained weighted linear least-squares problem is known to be a convex combination of the basic solutions formed by the nonsingular subsystems if the weight matrix is diagonal...
The solution of the unconstrained weighted linear least-squares problem is known to be a convex combination of the basic solutions formed by the nonsingular subsystems if the weight matrix is diagonal...
On the Dynamics of the Linear Process $Y( k ) = A ( k )Y ( k - 1 )$ with Irreducible Matrices $A( k )$
An upper bound is given for the projective distance $d( Y( k ),V ( k ) )$, where $Y( k ) = A( k )Y( k - 1 )$ is a nonautonomous linear process in the positive quadrant of $\mathbb{R}^n$($A( i )$ irred...
An upper bound is given for the projective distance $d( Y( k ),V ( k ) )$, where $Y( k ) = A( k )Y( k - 1 )$ is a nonautonomous linear process in the positive quadrant of $\mathbb{R}^n$($A( i )$ irred...
You are not logged in to this journal. Log in
Deflation Techniques for an Implicitly Restarted Arnoldi Iteration
SIAM. J. Matrix Anal. & Appl. Volume 17, Issue 4, pp. 789-821 (October 1996)
Issue Date: October 1996
Connotea
CiteULike
del.icio.us
BibSonomy
A deflation procedure is introduced that is designed to improve the convergence of an implicitly restarted Arnoldi iteration for computing a few eigenvalues of a large matrix. As the iteration progresses, the Ritz value approximations of the eigenvalues converge at different rates. A numerically stable scheme is introduced that implicitly deflates the converged approximations from the iteration. We present two forms of implicit deflation. The first, a locking operation, decouples converged Ritz values and associated vectors from the active part of the iteration. The second, a purging operation, removes unwanted but converged Ritz pairs. Convergence of the iteration is improved and a reduction in computational effort is also achieved. The deflation strategies make it possible to compute multiple or clustered eigenvalues with a single vector restart method. A block method is not required. These schemes are analyzed with respect to numerical stability, and computational results are presented.
©1996 (Copyright) Society for Industrial and Applied Mathematics
| History: | Received 1995-02-10; accepted 1995-11-08 |
| Permalink: | http://dx.doi.org/10.1137/S0895479895281484 |
KEYWORDS and AMS
65F15, 65G05
PUBLICATION DATA
0895-4798 (print)
1095-7162 (online)
SIAM