Dollar, H. Sue and Gould, Nicholas I. M. and Schilders, W. H. A. and Wathen, A. J. (2005) Using constraint preconditioners with regularized saddlepoint problems. Technical Report. Unspecified. (Submitted)

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Abstract
The problem of finding good preconditioners for the numerical solution of a certain important class of indefinite linear systems is considered. These systems are of a 2 by 2 block (KKT) structure in which the (2,2) block (denoted by C) is assumed to be nonzero. In Constraint preconditioning for indefinite linear systems , SIAM J. Matrix Anal. Appl., 21 (2000), Keller, Gould and Wathen introduced the idea of using constraint preconditioners that have a specific 2 by 2 block structure for the case of C being zero. We shall give results concerning the spectrum and form of the eigenvectors when a preconditioner of the form considered by Keller, Gould and Wathen is used but the system we wish to solve may have C 0 . In particular, the results presented here indicate clustering of eigenvalues and, hence, faster convergence of Krylov subspace iterative methods when the entries of C are small; such situations arise naturally in interior point methods for optimization and we present results for such problems which validate our conclusions.
The first author's work was supported by the OUCL Doctorial Training Account
Item Type:  Technical Report (Technical Report) 

Subjects:  H  N > Numerical analysis 
Research Groups:  Numerical Analysis Group 
ID Code:  1130 
Deposited By:  Lotti Ekert 
Deposited On:  12 May 2011 07:36 
Last Modified:  29 May 2015 18:49 
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