International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 25, Pages 1315-1327
doi:10.1155/S0161171204202265
A parallel Cholesky algorithm for the solution of symmetric
linear systems
Department of Mathematics and Computer Science, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait
Received 21 February 2002
Copyright © 2004 R. R. Khazal and M. M. Chawla. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
For the solution of symmetric linear systems, the classical
Cholesky method has proved to be difficult to parallelize. In the
present paper, we first describe an elimination variant of
Cholesky method to produce a lower triangular matrix which
reduces the coefficient matrix of the system to an identity
matrix. Then, this elimination method is combined with the partitioning method
to obtain a parallel Cholesky algorithm. The total
serial arithmetical operations count for the parallel algorithm
is of the same order as that for the serial Cholesky method. The
present parallel algorithm could thus perform with
efficiency close to 1 if implemented on a multiprocessor
machine. We also discuss the existence of the parallel
algorithm; it is shown that for a symmetric and positive definite
system, the presented parallel Cholesky algorithm is well defined
and will run to completion.