Fast and scalable parallel matrix computations with reconfigurable pipelined optical buses

Abstract

We present fast and highly scalable parallel computations for a number of important and fundamental matrix problems on linear arrays with reconfigurable pipelined optical bus systems. These problems include computing the powers, the inverse, the characteristic polynomial, the determinant, the rank and an LU- and a QR-factorization of a matrix; multiplying a chain of matrices; and solving linear systems of equations. These computations are based on efficient implementation of the fastest sequential matrix multiplication algorithm, and are highly scalable over a wide range of system size. Such fast and scalable parallel matrix computations were not seen before on distributed memory parallel computing systems.