# Parallel algorithms of the Purcell method for direct solution of linear systems

Chen, Ke and Lai, Choi H.
(2002)
*Parallel algorithms of the Purcell method for direct solution of linear systems.*
Parallel Computing, 28 (9).
pp. 1275-1291.
ISSN 0167-8191
(doi:10.1016/S0167-8191(02)00133-3)

## Abstract

In this paper, we first demonstrate that the classical Purcell's vector method when combined with row pivoting yields a consistently small growth factor in comparison to the well-known Gauss elimination method, the Gauss–Jordan method and the Gauss–Huard method with partial pivoting. We then present six parallel algorithms of the Purcell method that may be used for direct solution of linear systems. The algorithms differ in ways of pivoting and load balancing. We recommend algorithms V and VI for their reliability and algorithms III and IV for good load balance if local pivoting is acceptable. Some numerical results are presented.

Item Type: | Article |
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Uncontrolled Keywords: | linear systems, Purcell elimination method, Gauss–Huard method, parallel algorithms, distributed computing |

Subjects: | Q Science > QA Mathematics > QA76 Computer software |

Pre-2014 Departments: | School of Computing & Mathematical Sciences School of Computing & Mathematical Sciences > Centre for Numerical Modelling & Process Analysis School of Computing & Mathematical Sciences > Centre for Numerical Modelling & Process Analysis > Computational Science & Engineering Group School of Computing & Mathematical Sciences > Department of Mathematical Sciences |

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Last Modified: | 14 Oct 2016 09:02 |

URI: | http://gala.gre.ac.uk/id/eprint/952 |

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