期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2004
卷号：2004
DOI：10.1155/S0161171204202265
出版社：Hindawi Publishing Corporation
摘要：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.
