Systolic arrays for matrix over-relaxation methods

Abstract

This paper presents the systolic designs for the Jacobi Overrelaxation (J.O.R.), Successive Overrelaxation (S.O.R.), Accelerated Overrelaxation (A.O.R.), stationary and non-stationary second order Richardson methods for the iterative solution of large linear systems. The linear systems are obtained from the discretisation of a two and three dimensional Laplace equation by the finite difference method and the coefficient matrices are sparse symmetric and positive definite. We investigate the hardware implementation of a linear systolic array to achieve a low cost and optimal area efficient VLSI solution.