Triangular matrix inversion on systolic arrays

Abstract We study the systolic implementation of the algorithm which inverts a triangular matrix A of order n , by pipelining n linear systems of equation Ax h = e h , for h = 1,…, n , where e h denotes the h th vector of the canonical basis. It is known that the time complexity of the problem is T = 2 n − 1. We show that the minimum number S∗ of processors required to solve the problem in optimal time is such thatn n 2 /8.5 + O (n) ⩽ S∗⩽ n 2 /6 + O (n) . The upper bound is obtained by exhibiting and hexagonally connected systolic array with 1 6 n 2 + O (n) cells. This array improves all previously known solutions.