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Preprint 8-2018

A robust iterative scheme for symmetric indefinite systems

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Author(s) : Murat Manguglu , Volker Mehrmann

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 8-2018

MSC 2000

65F10 Iterative methods for linear systems
65F15 Eigenvalues, eigenvectors

Abstract :
We propose a two-level nested preconditioned iterative scheme for solving sparse linear systems of equations in which the coefficient matrix is symmetric and indefinite with relatively small number of negative eigenvalues. The proposed scheme consists of an outer Minimum Residual (MINRES) iteration, preconditioned by an inner Conjugate Gradient (CG) iteration in which CG can be further preconditioned. The robustness of the proposed scheme is illustrated by solving indefinite linear systems that arise in the solution of quadratic eigenvalue problems in the context of model reduction methods for finite element models of disk brakes as well as on other problems that arise in a variety of applications.

Keywords : symmetric indefinite systems, Krylov subspace method, sparse linear systems, deflation, preconditioned minimum residual method, preconditioned conjugate gradient method

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