A systolic array design for matrix system solution by the symmetric bordering method

Abstract

The idea of symmetric bordering is a new strategy introduced by Evans and Levin [1] for the inversion of a full matrix, although as a special case the solution of a linear system can be found. The aim of this paper is to demonstrate that symmetric bordering can be performed by a systolic array and that the technique is more efficient than previous arrays for computing the matrix inverse and the solution of linear systems by elimination techniques. Symmetric bordering is a similar concept to the well known bordering methods, except that the bordering strategy is applied to the left hand top and bottom right hand elements of the matrix simultaneously. The amount of parallelism has been shown to be superior to that achieved by the Gauss Jordan algorithm [1].