A. Bouras and V. Fraysse, "A Relaxation Strategy for the Arnoldi Method in Eigenproblems," CERFACS TR/PA/00/16, European Centre for Research and Advanced Training in Scientific Computation, Toulouse, France (2000). Home/Search Document Details and Download
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A Relaxation Strategy for Inner-Outer Linear Solvers in.. - Amina Bouras Val (2000) (6 citations) Self-citation (Bouras Frayss) (Correct)
.... for inner outer linear solvers in domain decomposition methods Amina Bouras Val erie Frayss e y Luc Giraud y CERFACS Technical Report TR PA 00 17 Abstract The remarkable robustness of Krylov methods with respect to inexact matrixvector products is a strong property recently emphasised [11, 2, 3]. In the context of embedded iterative solvers with an outer Krylov scheme, it is possible to monitor the inner accuracy and relax it when outer convergence proceeds. We extend the relaxation strategy proposed in [2] to the context of domain decomposition methods for partial di erential equations ....
....when the outer process comes closer to the solution. The proposed strategies for monitoring the inner iterations have been so far very problem and method dependent. More recently in the late nineties, the di erent behaviour of embedded solvers involving a Krylov outer process has been emphasised [11, 9, 2, 3]. Surprisingly, it is observed that the rst Krylov vectors need to be known with full accuracy, and this accuracy can be signi cantly relaxed as the convergence proceeds. In [9] inner outer iterations for the Conjugate Gradient are studied Universit e Toulouse I and CERFACS, 42 av. Gaspard ....
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A. Bouras and V. Fraysse. A relaxation strategy for the Arnoldi method in eigenproblems. Technical Report TR/PA/00/16, CERFACS, Toulouse, France, 2000.
A relaxation strategy for inexact matrix-vector products.. - Bouras, Frayssé (2000) (8 citations) Self-citation (Bouras Frayss) (Correct)
.... Universit e Toulouse I and CERFACS, 42 av. Gaspard Coriolis, 31057 Toulouse cedex 1. Email: bouras cerfacs.fr. The work of this author was supported by CNES (Centre National d Etudes Spatiales) y CERFACS, 42 av. Gaspard Coriolis, 31057 Toulouse cedex 1. Email: fraysse cerfacs.fr 1 and in [1] for non symmetric matrices. It is observed, as for Newton like methods, that inverse iterations require inner iterations to be more and more accurate while approaching the solution. But for Lanczos or Arnoldi method methods on the contrary, the rst Krylov vectors need to be known with full ....
....one uses an approximate linear solver (such as an iterative method) the approximate solution z satis es (A A k ) z = v k . Again, it is possible to relax the accuracy on z as long as the outer process converges so that both the cost of the inner iterations and the global cost are reduced [1]. Another application of importance arises in the context of domain decomposition methods for partial di erential equations. For large problems, the local subproblems induced by the decomposition have to be solved by an iterative process which is embedded in the outer iterative process that ....
[Article contains additional citation context not shown here]
A. Bouras and V. Fraysse. A relaxation strategy for the Arnoldi method in eigenproblems. Technical Report TR/PA/00/16, CERFACS, Toulouse, France, 2000.
Krylov Subspace Iterations for Deterministic.. - Warsa, Wareing.. (Correct)
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A. Bouras and V. Fraysse, "A Relaxation Strategy for the Arnoldi Method in Eigenproblems," CERFACS TR/PA/00/16, European Centre for Research and Advanced Training in Scientific Computation, Toulouse, France (2000).
Theory of Inexact Krylov Subspace Methods and Applications.. - Simoncini, Szyld (2002) (2 citations) (Correct)
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A. Bouras and V. Fraysse. A relaxation strategy for the Arnoldi method in eigenproblems. Technical Report TR/PA/00/16, CERFACS, Toulouse, France, 2000.
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