Sparse Givens QR Factorization on a Multiprocessor

Abstract

[Abstract] We present a parallel algorithm for the QR factorization with column pivoting of a sparse matrix by means of Givens rotations. Nonzero elements of the matrix M to be decomposed are stored in a one dimensional doubly linked list data struct1tre. We will discuss a strategy to reduce fill-in in order to gain memory savings and decrease the computation times. As an application of QR factorization, we will describe the least squares problem. This algorithm has been designed for a message passing multiprocessor and we have evaluated it on the Cray T3D supercomputer using the Harwell-Boeing sparse matrix collection.