Optimal matrix algorithms on homogeneous hypercubes

Abstract

This paper describes a set of concurrent algorithms for matrix algebra, based on a library of collective communication routines for the hypercube. We show how a systematic application of scattering reduces load imbalance. A number of examples are considered (Gaussian elimination, Gauss-Jordan matrix inversion, the power method for eigenvectors, and tridiagonalisation by Householder's method), and the concurrent efficiencies are discussed.