Parallelizing Sylvester-like Operations on a Distributed Memory Computer

A SIMD scheme for parallelization of the 2-D array operation M(x) = (D×A + B×I + V) x is developed for a distributed memory computer with 2-D mesh processor network. This scheme is carefully designed in order to approach the best possible speed-up by avoiding unnecessary message communication. The numerical results on a Touchstone DELTA machine are presented to demonstrate the effectiveness of the scheme. This scheme can be generalized to one that would deal with the 3-D array operation M3D(x) + (I×I×A + I×B×I + C×I×I + V) x on a distributed memory computer with 3-D torus processor network