Parallel algorithms for solution of tridiagonal systems on multicomputers

Authors:
Xian-He Sun;Hong Zhang Sun;Lionel M. Ni
Affiliations:
Department of Mathematics, Michigan State University, East Lansing, MI;-;Department of Computer Science, Michigan State University, East Lansing, MI
Venue:
ICS '89 Proceedings of the 3rd international conference on Supercomputing
Year:
1989

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Abstract

Three parallel algorithms, namely the parallel partition LU (PPT) algorithm, the parallel partition hybrid (PPH) algorithm, and the parallel diagonal dominant (PDD) algorithm are proposed for solving tridiagonal linear systems on multicomputers. These algorithms are based on the divide-and-conquer parallel computation model. The PPT and PPH algorithms support both pivoting and non-pivoting. The PPT algorithm is good when the number of processors is small; otherwise, the PPH algorithm is better. When the system is diagonal dominant, the PDD algorithm is highly parallel and provides an approximate solution which equals to the exact solution within machine accuracy. Both computation and communication complexities of the three algorithms are presented. All three methods proposed in this paper outperform other known parallel algorithms and have been implemented on a 64-node Ncube multicomputer. The analytic results matches closely with the results measured from the Ncube machine.