Prefix algorithms for tridiagonal systems on hypercube multiprocessors

Abstract

The recursive doubling algorithm as developed by Stone can be used to solve a tridiagonal linear system of size n on a parallel computer with n processors using &Ogr; ( log n ) parallel arithmetic steps. Here we describe a limited processor version of the recursive doubling algorithm for the solution of tridiagonal linear systems using &Ogr; ( n / p + log p ) parallel arithmetic steps on a parallel computer with p < n processors. The main technique relies on fast parallel prefix algorithms, which can be efficiently mapped on the hypercube architecture using the binary-reflected Gray code. For pn this algorithm achieves linear speed-up and constant efficiency over its sequential implementation as well as over the sequential LU decomposition algorithm. These results are confirmed by numerical experiments obtained on an Intel iPSC/d5 hypercube multiprocessor.