Geodesic
Improved convergence bounds for smoothed aggregation method: linear dependence of the convergence rate on the number of levels
Czechoslovak Mathematical Journal, Tome 66 (2016) no. 3, pp. 829-845
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The smoothed aggregation method has became a widely used tool for solving the linear systems arising by the discretization of elliptic partial differential equations and their singular perturbations. The smoothed aggregation method is an algebraic multigrid technique where the prolongators are constructed in two steps. First, the tentative prolongator is constructed by the aggregation (or, the generalized aggregation) method. Then, the range of the tentative prolongator is smoothed by a sparse linear prolongator smoother. The tentative prolongator is responsible for the approximation, while the prolongator smoother enforces the smoothness of the coarse-level basis functions.
The smoothed aggregation method has became a widely used tool for solving the linear systems arising by the discretization of elliptic partial differential equations and their singular perturbations. The smoothed aggregation method is an algebraic multigrid technique where the prolongators are constructed in two steps. First, the tentative prolongator is constructed by the aggregation (or, the generalized aggregation) method. Then, the range of the tentative prolongator is smoothed by a sparse linear prolongator smoother. The tentative prolongator is responsible for the approximation, while the prolongator smoother enforces the smoothness of the coarse-level basis functions.
DOI : 10.1007/s10587-016-0295-5
Classification : 65F10, 65N12, 65N55
Keywords: smoothed aggregation; improved convergence bound 
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Brousek, Jan; Fraňková, Pavla; Vaněk, Petr. Improved convergence bounds for smoothed aggregation method: linear dependence of the convergence rate on the number of levels. Czechoslovak Mathematical Journal, Tome 66 (2016) no. 3, pp. 829-845. doi: 10.1007/s10587-016-0295-5

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