Solution of sparse positive definite systems on a hypercube

Abstract

The solution of large sparse positive definite systems of equations typically involves four steps: ordering, data structure set-up (symbolic factorization), numerical factorization, and triangular solution. This article describes how these four phases are implemented on a hypercube multiprocessor. The role of elimination trees in the exploitation of sparsity and the identification of parallelism is explained, and pseudo-code algorithms are provided for some of the important algorithms. Numerical experiments run on an Intel iPSC multiprocessor are presented in order to provide some indication of the performance of the various algorithms.