A new Parallel algorithm for solving general linear systems of equations

Abstract

A new parallel direct algorithm for solving general linear systems of equations ist proposed in this paper. For sparse systems our algorithm requires less computations than the classical Jordan algorithm. Particularly we have also derived two related algorithms for linear recurrence problems of order 1 and tridiagonal systems. Each of the two algorithms has the same computational complexity as that of the corresponding recursive doubling algorithm or Even/Odd elimination algorithm, but requires half of the processors required by the corresponding algorithm.

The numerical experiments on the vector computer YH-1 indicate that, as the number of equations of a tridiagonal system increases, the speedup of our algorithm over the Even/Odd algorithm increases, and the maximum speedup is more than 3.