turkmath.org

Sparse linear systems of equations that are symmetric and indefinite are an important class of problems that arise in a variety of applications including optimization, computational physics and chemistry. We propose a novel 2-level nested Krylov subspace scheme for symmetric indefinite systems where the coefficient matrix has only few negative eigenvalues. The proposed scheme consists of outer Minimum Residual (MINRES) iterations with a deflated preconditioner. Deflated systems involving the preconditioner are solved via inner Conjugate Gradient (CG) iterations with an indefinite preconditioner. The robustness of the proposed scheme is illustrated via realistic linear systems that arise in a variety of applications.