Algorithms for LU decomposition on a shared memory multiprocessor

Abstract

In this paper we propose an improved algorithm for the parallel LU decomposition of an ( m + 1)-banded upper Hessenberg matrix on a shared memory multi-processor, which requires O(2 nm 2/ p) parallel operations, where n is the dimension of the matrix and p is the number of processors. We show that for the special case of tridiagonal matrices this algorithms has a lower operation count than those in the literature and yields the best existing algorithm for the solution of tridiagonal systems of equations.