Efficient preconditioner updates for shifted linear systems

We present a new technique for building effective and low cost preconditioners for sequences of shifted linear systems (A+aI)x=b, where A is symmetric positive definite and a>0. This technique updates a preconditioner for A, available in the form of an LDL' factorization, by modifying only the nonzero entries of the L factor in such a way that the resulting preconditioner mimics the diagonal of the shifted matrix and reproduces its overall behaviour. The proposed approach is supported by a theoretical analysis as well as by numerical experiments, showing that it works efficiently for a broad range of values of a.

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Preprint n. 5/2010, Department of Mathematics, Second University of Naples, Caserta, Italy, July 2010

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