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 Nth power, the inverse, 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.KeywordsCharacteristic PolynomialTriangular MatrixLower Triangular MatrixMatrix PowerParallel MatrixThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.