## Abstract

In this work, we consider the problem of solving x ^{(k)} =b ^{(k)}, k= 1,...K,where b ^{(k+1)} = f(x ^{(k)}). We show that when A is a full n × n matrix and K ≥cn, where c≦ 1 depends on the specific software and hardware setup, it is faster to solve Ax ^{(k)} =b ^{(k)} for k = 1,...K by explicitly evaluating the inverse matrix A ^{-1} rather than through the LU decomposition of A. We also show that the forward error is comparable in both methods, regardless of the condition number of A.

Original language | English |
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Pages (from-to) | 29-44 |

Number of pages | 16 |

Journal | Journal of Scientific Computing |

Volume | 32 |

Issue number | 1 |

DOIs | |

State | Published - Jul 2007 |

## Keywords

- Linear systems
- Matrix inversion

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