### Abstract

Original language | Undefined |
---|---|

Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Number of pages | 8 |

Publication status | Published - Dec 2011 |

### Publication series

Name | Memorandum / Department of Applied Mathematics |
---|---|

Publisher | University of Twente, Department of Applied Mathematics |

No. | 1971 |

ISSN (Print) | 1874-4850 |

ISSN (Electronic) | 1874-4850 |

### Keywords

- IR-79127
- Complexity
- Perfect elimination
- METIS-284946
- Gaussian elimination
- Bipartite graph
- EWI-21127

### Cite this

*A note on perfect partial elimination*. (Memorandum / Department of Applied Mathematics; No. 1971). Enschede: University of Twente, Department of Applied Mathematics.

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*A note on perfect partial elimination*. Memorandum / Department of Applied Mathematics, no. 1971, University of Twente, Department of Applied Mathematics, Enschede.

**A note on perfect partial elimination.** / Bomhoff, M.J.; Kern, Walter; Still, Georg J.

Research output: Book/Report › Report › Professional

TY - BOOK

T1 - A note on perfect partial elimination

AU - Bomhoff, M.J.

AU - Kern, Walter

AU - Still, Georg J.

N1 - eemcs-eprint-21127

PY - 2011/12

Y1 - 2011/12

N2 - In Gaussian elimination it is often desirable to preserve existing zeros (sparsity). This is closely related to perfect elimination schemes on graphs. Such schemes can be found in polynomial time. Gaussian elimination uses a pivot for each column, so opportunities for preserving sparsity can be missed. In this paper we consider a more flexible process that selects a pivot for each nonzero to be eliminated and show that recognizing matrices that allow such perfect partial elimination schemes is NP-hard.

AB - In Gaussian elimination it is often desirable to preserve existing zeros (sparsity). This is closely related to perfect elimination schemes on graphs. Such schemes can be found in polynomial time. Gaussian elimination uses a pivot for each column, so opportunities for preserving sparsity can be missed. In this paper we consider a more flexible process that selects a pivot for each nonzero to be eliminated and show that recognizing matrices that allow such perfect partial elimination schemes is NP-hard.

KW - IR-79127

KW - Complexity

KW - Perfect elimination

KW - METIS-284946

KW - Gaussian elimination

KW - Bipartite graph

KW - EWI-21127

M3 - Report

T3 - Memorandum / Department of Applied Mathematics

BT - A note on perfect partial elimination

PB - University of Twente, Department of Applied Mathematics

CY - Enschede

ER -