New Fast Algorithms for First-Order Linear Recurrences on Vector Computers

Abstract

We examine the performance of parallel algorithms for first-order linear recurrence on vector computers, evaluate them quantitatively on a simple model of vector computers, and propose new fast algorithms. We also show a result of performance benchmarking of them on actual vector computers. 1 Introduction First-order linear recurrence is a basic operation often used in many algorithms of numerical analysis such as solving general block diagonal linear system. But it is also a notorious example such that we cannot get good performance on vector supercomputers. Since naive vectorization of first-order recurrence is impossible, some Japanese supercomputers have special hardware support for it. But the performance is still not so much as that for ordinary element-wise operations. On the other hand, there have been proposed many parallel algorithms for first-order recurrences [4], and some of them are tuned for vector computers [12, 14]. However, many of them cannot achieve enough perform..