A parallel/recursive algorithm

Abstract

An algorithm is discussed for converting a class of recursive processes to a parallel system. It is argued that this algorithm can be superior to certain methods currently found in the literature for an important subset of problems. The cases of homogeneous and non-homogeneous two term recursions are treated. The basic cost factor of the algorithm over non-parallel operations is 2 if only the final values of the sequence is needed and 4 if all elements are required. In practice, these factors can be reduced considerably. Applications to three problems (finding the eigenvalues of a tri-diagonal matrix, the solution of a radial wave equation and the solution of a tri-diagonal matrix) are discussed.