Abstract
The preconditioning of generalized conjugate gradient methods by means of data reduction (DARE) methods for linear systems arising from the finite difference method will be presented. DARE is a multilevel method where unknowns are dropped by using a functional approach. On each level iterations of generalized CG methods are performed according to different strategies. The better the functional approach fits the solution, i.e. the finer the size of the grid compared to the solution curvature, the better DARE works. Numerical experiments show that one gets a nearly linear increase in computation with the number of unknowns and that the convergence of DARE is rather independent from the operator of the partial differential equation. DARE turns out to be a promising and feasible technique, but a lot of work still has to be done looking for optimal strategies.
Keywords
- Multigrid Method
- Newton Step
- Vector Computer
- Multilevel Method
- Large Linear System
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© 1990 Springer-Verlag
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Weiss, R., Schönauer, W. (1990). Data reduction (dare) preconditioning for generalized conjugate gradient methods. In: Axelsson, O., Kolotilina, L.Y. (eds) Preconditioned Conjugate Gradient Methods. Lecture Notes in Mathematics, vol 1457. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090906
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DOI: https://doi.org/10.1007/BFb0090906
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Publisher Name: Springer, Berlin, Heidelberg
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Online ISBN: 978-3-540-46746-5
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