Fast and scalable parallel matrix computations with 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 N th power, the in verse, the characteristic polynomial, the determinant, the rank, and an LU- and a QR-factorization of a matrix, 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. © 2000 Springer-Verlag Berlin Heidelberg.