Given's rotation on an instruction systolic array

Abstract

In this paper we show that the concept of instruction systolic arrays allows to implement efficiently a transformation scheme for triangularizing rectangular m×n-matrices using Given's rotations. Based on a careful choice of an appropriate set of instructions, a program for the instruction systolic array can be designed having a time complexity of O(min(n,m-1)). Although the instruction systolic array allows for much greater flexibility, the time complexity is of the same order as that of the special purpose triangular systolic array designed by Gentleman and Kung.