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Section: New Results

A Class of Efficient Locally Constructed Preconditioners Based on Coarse Spaces

In [24] we present a class of robust and fully algebraic two-level preconditioners for SPD matrices. We introduce the notion of algebraic local SPSD splitting of an SPD matrix and we give a characterization of this splitting. It helps construct algebraically and locally a class of efficient coarse subspaces which bound the spectral condition number of the preconditioned system by a number defined a priori. Some PDEs-dependant preconditioners correspond to a special case of the splitting. The examples of the algebraic coarse subspaces in this paper are not practical due to expensive construction. We propose an heuristic approximation that is not costly. Numerical experiments illustrate the efficiency of the proposed method.