A new parallel algorithm for lagrange interpolation on a hypercube

Abstract

We present a new parallel algorithm for computing N point lagrange interpolation on an n-dimensional hypercube with total number of nodes p = 2 n. Initially, we consider the case when N = p. The algorithm is extended to the case when only p (p fixed) processors are available, p < N. We assume that N is exactly divisible by p. By dividing the hypercube into subcubes of dimension two, we compute the products and sums appearing in Lagrange's formula in a novel way such that wasteful repetitions of forming products are avoided. The speed up and efficiency of our algorithm is calculated both theoretically and by simulating it over a network of PCs. (~)