SCHEDULING OF THE DAG ASSOCIATED WITH PIPELINE INVERSION OF TRIANGULAR MATRICES

Abstract

We are interested in methods which compute the inverse of a triangular matrix A of order n by solving the n linear systems Ax=ei, i=1,…, n, where ei is the i-th element of the canonical basis of Rn. More precisely, we consider the dependence graph associated with algorithms where the entries of matrix A are read only once and used in pipeline for the solution of these systems. We exhibit a new scheduling which induces an algorithm with time complexity T*=2n−1. The number n2/8+O(n) of processors required by this scheduling improves the best previously known bound n2/6+O(n), and is quite close to the lower bound n2/8.5+O(n).