Communication and matrix computations on large message passing systems

abstract This paper is concerned with the consequences for matrix computations of having a rather large number of general purpose processors, say ten or twenty thousand, connected in a network in such a way that a processor can communicate only with its immediate neighbors. Certain communication tasks associated with most matrix algorithms are deened and formulas developed for the time required to perform them under several communication regimes. The results are compared with the times for a nominal n 3 oating point operations. The results suggest that it is possible to use a large number of processors to solve matrix problems at a relatively ne granularity, provided ne grain communication is available.