The Mathematical Institute, University of Oxford, Eprints Archive

On choice of preconditioner for minimum residual methods for nonsymmetric matrices

Pestana, Jennifer and Wathen, A. J. (2011) On choice of preconditioner for minimum residual methods for nonsymmetric matrices. Technical Report. SIMAX. (Submitted)

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Abstract

Existing convergence bounds for Krylov subspace methods such as GMRES for nonsymmetric linear systems give little mathematical guidance for the choice of preconditioner. Here, we establish a desirable mathematical property of a preconditioner which indicates when convergence of a minimum residual method will essentially depend only on the eigenvalues of the preconditioned system, as is true in the symmetric case. Our theory covers the generic case of nonsymmetric coefficient matrices which are diagonalisable
over C; it does not cover matrices with nontrivial Jordan form.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1070
Deposited By:Lotti Ekert
Deposited On:06 May 2011 08:23
Last Modified:06 May 2011 08:23

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