Parallel solution of sparse linear least squares problems on distributed-memory multiprocessors

Abstract

This paper studies the parallel solution of large-scale sparse linear least squares problems on distributed-memory multiprocessors. The key components required for solving a sparse linear least squares problem are sparse QR factorization and sparse triangular solution. A block-oriented parallel algorithm for sparse QR factorization has already been described in the literature. In this paper, new block-oriented parallel algorithms for sparse triangular solution are proposed. The arithmetic and communication complexities of the new algorithms applied to regular grid problems are analyzed. The proposed parallel sparse triangular solution algorithms together with the block-oriented parallel sparse QR factorization algorithm result in a highly efficient approach to the parallel solution of sparse linear least squares problems. Performance results obtained on an IBM Scalable POWERparallel system SP2 are presented. The largest least squares problem solved has over two million rows and more than a quarter million columns. The execution speed for the numerical factorization of this problem achieves over 3.7 gigaflops per second on an IBM SP2 machine with 128 processors.