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Efficient preconditioner updates for shifted linear systems

Stefania Bellavia (stefania.bellavia***at***unifi.it)
Valentina De Simone (valentina.desimone***at***unina2.it)
Daniela di Serafino (daniela.diserafino***at***unina2.it)
Benedetta Morini (benedetta.morini***at***unifi.it)

Abstract: 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.

Keywords: shifted linear systems, preconditioner updates, incomplete LDL' factorization

Category 1: Nonlinear Optimization (Nonlinear Systems and Least-Squares )

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

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Entry Submitted: 07/23/2010
Entry Accepted: 07/23/2010
Entry Last Modified: 07/23/2010

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