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

Authors:
Ke Chen;Choi H. Lai
Affiliations:
Department of Mathematical Sciences, University of Liverpool, Peach Street, Liverpool L69 7ZL, UK;School of Computing and Mathematical Sciences, University of Greenwich, Wellington Street, Woolwich, London SE18 6PF, UK
Venue:
Parallel Computing
Year:
2002

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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.