A parallel QR factorization algorithm using local pivoting

A parallel version of the Householder algorithm with column pivoting is introduced for computing the QR factorization of a matrix. Local pivoting allows efficient implementation of the algorithm on a parallel machine; in particular, it is implemented on one with a distributed architecture. An inexpensive but reliable incremental condition estimator is used to control the selection of pivot columns by obtaining cheap estimates for the smallest singular value of the currently created upper triangular matrix R. Numerical experiments show that the local pivoting strategy behaves about as well as the traditional global pivoting strategy. They also show the advantages of incorporating the controlled pivoting strategy into the traditional QR algorithm to guard against the known pathological cases