New Convergence Analysis of GMRES with Weighted Norms, Preconditioning and Deflation, Leading to a New Deflation Space
Résumé
New convergence bounds are presented for weighted, preconditioned, and deflated GMRES for the solution of large, sparse, 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 new bounds are a novel contribution in and of themselves. In addition, they are sufficiently explicit to indicate how to choose the preconditioner and the deflation space to accelerate the convergence. One such choice of deflating space is presented, and numerical experiments illustrate the effectiveness of such space.
Mots clés
- preconditioning
- 68W40
- 65Y05
- deflation AMS Subject Classification: 65F10
- linear solver
- linear solver convergence analysis domain decomposition deflation space preconditioning deflation AMS Subject Classification: 65F10 65Y05 68W40
- deflation
- deflation space
- domain decomposition
- convergence analysis
- GMRES
Domaines
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