Reducing communication costs in the conjugate gradient algorithm on distributed memory multiprocessors

Publisher Website
Google Scholar
Abstract
The standard formulation of the conjugate gradient algorithm involves two inner product computations. The results of these two inner products are needed to update the search direction and the computed solution. In a distributed memory parallel environment, the computation and subsequent distribution of these two values requires two separate communication and synchronization phases. In this paper, we present a mathematically equivalent rearrangement of the standard algorithm that reduces the number of communication phases. We give a second derivation of the modified conjugate gradient algorithm in terms of the natural relationship with the underlying Lanczos process. We also present empirical evidence of the stability of this modified algorithm.

This publication has 0 references indexed in Scilit: