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"We are concerned with the development of Algebraic Multigrid (AMG) for symmetric, positive definite linear systems arizing from finite element discretization of elliptic partial differential equations. AMG methods attempt to create coarse levels from the algebraic system automatically, using no or only a minimum of additional information. The basic idea of the multigrid algorithm is that fine level error on which the smoothing process is not effective should be reduced by the coarse correction. Therefore, a-priori estimates of the approximation of fine level functions by coarse level function are important to guide the design of robust AMG methods."
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