A ROBUST ITERATIVE SCHEME FOR SYMMETRIC INDEFINITE SYSTEMS

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Manguoglu M., Mehrmann V.

SIAM JOURNAL ON SCIENTIFIC COMPUTING, vol.41, no.3, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 41 Issue: 3
  • Publication Date: 2019
  • Doi Number: 10.1137/18m1190860
  • Journal Name: SIAM JOURNAL ON SCIENTIFIC COMPUTING
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: symmetric indefinite systems, Krylov subspace methods, sparse linear systems, preconditioned minimum residual method, preconditioned conjugate gradient method, deflation, KRYLOV SUBSPACE METHODS, PRECONDITIONERS, GMRES
  • Middle East Technical University Affiliated: Yes

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 a 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.