A Deflation Technique for Linear Systems of Equations

Authors:
K. Burrage;J. Erhel;B. Pohl;A. Williams
Affiliations:
-;-;-;-
Venue:
SIAM Journal on Scientific Computing
Year:
1998

Citing 0
Cited 3

Adaptive preconditioners for nonlinear systems of equations

Journal of Computational and Applied Mathematics
GMRES with adaptively deflated restarting and its performance on an electromagnetic cavity problem

Applied Numerical Mathematics
Newton-Picard-Based Preconditioning for Linear-Quadratic Optimization Problems with Time-Periodic Parabolic PDE Constraints

SIAM Journal on Scientific Computing

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Abstract

Iterative methods for solving linear systems of equations can be very efficient if the structure of the coefficient matrix can be exploited to accelerate the convergence of the iterative process. However, for classes of problems for which suitable preconditioners cannot be found or for which the iteration scheme does not converge, iterative techniques may be inappropriate. This paper proposes a technique for deflating the eigenvalues and associated eigenvectors of the iteration matrix which either slow down convergence or cause divergence. This process is completely general and works by approximating the eigenspace ${\Bbb P}$ corresponding to the unstable or slowly converging modes and then applying a coupled iteration scheme on ${\Bbb P}$ and its orthogonal complement ${\Bbb Q}$.