Analysis of a Class of Parallel Matrix Multiplication Algorithms

A Technical Paper Submitted to IPPS 98 y Abstract Publications concerning parallel implementation of matrix-matrix multiplication continue to appear with some regularity. It may seem odd that an algorithm that can be expressed as one statement and three nested loops deserves this much attention. This paper provides some insights as to why this problem is complex: Practical algorithms that use matrix multiplication tend to use diierent shaped matrices, and the shape of the matrices can signiicantly impact the performance of matrix multiplication. We provide theoretical analysis and experimental results to explain the diierences in performance achieved when these algorithms are applied to diierently shaped matrices. This analysis sets the stage for hybrid algorithms which choose between the algorithms based on the shapes of the matrices involved. While the paper resolves a number of issues, it concludes with discussion of a number of directions yet to be pursued. y Regarding the length of this paper: There are a large number of tables and gures within the text, in addition to an extensive bibliography. Taking this into account, the length is within submission guidelines.