Orateur
Description
This is joint work with Daniel Szyld (Temple University)
We present new convergence bounds for weighted, preconditioned, and deflated GMRES applied to non-Hermitian linear systems. These bounds are given for the case when the Hermitian part of the coefficient matrix is positive definite, the preconditioner is Hermitian positive definite, and the weight is equal to the preconditioner. The decrease in residual is bounded with respect to:
- the condition number of the preconditioned Hermitian part of the problem matrix,
- certain measure of how non-Hermitian the problem is. This indicates how to choose the preconditioner and the deflation space in order to accelerate convergence. One such choice of deflation space is proposed, and numerical experiments illustrate the effectiveness of such space.
