## Abstract

A two-phase preconditioning strategy based on a factored sparse approximate inverse is proposed for solving sparse indefinite matrices. In each phase, the strategy first makes the original matrix diagonally dominant to enhance the stability by a shifting method, and constructs an inverse approximation of the shifted matrix by utilizing a factored sparse approximate inverse preconditioner. The two inverse approximation matrices produced from each phase are then combined to be used as a preconditioner. Experimental results show that the presented strategy improves the accuracy and the stability of the preconditioner on solving indefinite sparse matrices. Furthermore, the strategy ensures that convergence rate of the preconditioned iterations of the two-phase preconditioning strategy is much better than that of the standard sparse approximate inverse ones for solving indefinite matrices.

Original language | English |
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Pages (from-to) | 1152-1159 |

Number of pages | 8 |

Journal | Computers and Mathematics with Applications |

Volume | 58 |

Issue number | 6 |

DOIs | |

State | Published - Sep 2009 |

## Keywords

- Factored sparse approximate inverse
- Indefinite matrix
- Preconditioning

## ASJC Scopus subject areas

- Modeling and Simulation
- Computational Theory and Mathematics
- Computational Mathematics