This paper introduces a robust preconditioner for general sparse symmetricmatrices, that is based on low-rank approximations of the Schur complement in aDomain Decomposition (DD) framework. In this "Schur Low Rank" (SLR)preconditioning approach, the coefficient matrix is first decoupled by DD, andthen a low-rank correction is exploited to compute an approximate inverse ofthe Schur complement associated with the interface points. The method avoidsexplicit formation of the Schur complement matrix. We show the feasibility ofthis strategy for a model problem, and conduct a detailed spectral analysis forthe relationship between the low-rank correction and the quality of thepreconditioning. Numerical experiments on general matrices illustrate therobustness and efficiency of the proposed approach.
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