### Abstract

Gaussian elimination with partial pivoting achieved by adding the pivot row to the kth row at step k, was introduced by Onaga and Takechi in 1986 as a means for reducing communications in parallel implementations. In this paper it is shown that the growth factor of this partial pivoting algorithm is bounded above by μ_{n} < 3^{n-1}, as compared to 2^{n-1} for the standard partial pivoting. This bound μ_{n}, close to 3^{n-2}, is attainable for a class of near-singular matrices. Moreover, for the same matrices the growth factor is small under partial pivoting.

Original language | English (US) |
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Pages (from-to) | 633-639 |

Number of pages | 7 |

Journal | BIT Numerical Mathematics |

Volume | 41 |

Issue number | 3 |

DOIs | |

State | Published - Sep 2001 |

### Keywords

- Gaussian elimination
- Growth factor
- Parallel algorithm
- Stability

### ASJC Scopus subject areas

- Software
- Computer Networks and Communications
- Computational Mathematics
- Applied Mathematics

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## Cite this

Mead, J. L., Renaut, R., & Welfert, B. (2001). Stability of a pivoting strategy for parallel Gaussian elimination.

*BIT Numerical Mathematics*,*41*(3), 633-639. https://doi.org/10.1023/A:1021931632067