A Parallel Ordering for the Block Jacobi Method on a Hypercube Architecture

Abstract

Jacobi methods for computing the singular value decomposition are ideally suited for multiprocessor environments since they contain a great deal of inherent parallelism. We give a parallel ordering for the block Jacobi Method that allows us to take full advantage of the nearest-neighbor topology of the hypercube. It is based on recursively embedding smaller rings into the hypercube using a Gray code labelling of processor nodes. This scheme is optimal in that it entails the lowest communication overhead possible.