A numerical study of optimized sparse preconditioners
The authors are concerned with the existence of optimized preconditioners of either Cholesky factored form or of polynomial form for the preconditioned conjugate gradient method applied to linear systems with symmetric, positive definite coefficient matrices. The Fourier approach for a discretized 2D Poisson equation as a model problem allows the explicit knowledge of the spectrum of the preconditioned stiffness matrix which is the basis to establish specific criteria for the selection of the preconditioner in terms of object functions depending on the preconditioner's parameters. The performance of the resulting preconditioners is investigated by extensive numerical experiments. In accordance with the theory, the main findings are that optimized preconditioners can lead to a reduction of the number of conjugate gradient iterations, but leave the asymptotic convergence rate unchanged.
preconditioned conjugate gradient method
scientific article; zbMATH DE number 644787
scientific article