### Abstract

For the iterative solution of saddle point problems, a nonsymmetric preconditioner is studied which, with respect to the upper-left block of the system matrix, can be seen as a variant of SSOR. An idealized situation where SSOR is taken with respect to the skew-symmetric part plus the diagonal part of the upper-left block is analyzed in detail. Since action of the preconditioner involves solution of a Schur complement system, an inexact form of the preconditioner can be of interest. This results in an inner-outer iterative process. Numerical experiments with solution of linearized Navier-Stokes equations demonstrate the efficiency of the new preconditioner, especially when the upper-left block is far from symmetric.

Original language | Undefined |
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Article number | 10.1137/040618680 |

Pages (from-to) | 1125-1149 |

Number of pages | 25 |

Journal | SIAM journal on matrix analysis and applications |

Volume | 27 |

Issue number | Technical/4 |

DOIs | |

Publication status | Published - 2006 |

### Keywords

- MSC-65F22
- MSC-65F35
- MSC-65K10
- MSC-65N22
- Navier Stokes equations
- SSOR
- nonsymmetric indefinite linear systems
- inner-outer iterations
- iterative methods
- constraint preconditioners
- skew-symmetric preconditioners
- preconditioning methods
- saddle point problems
- EWI-8959
- MSC-65F10
- METIS-237883
- IR-66838

## Cite this

Bochev, M. A., & Golub, G. H. (2006). A Class of Nonsymmetric Preconditioners for Saddle Point Problems.

*SIAM journal on matrix analysis and applications*,*27*(Technical/4), 1125-1149. [10.1137/040618680]. https://doi.org/10.1137/040618680