LAPACK-style codes for pivoted Cholesky and QR updating

Authors:
Sven Hammarling;Nicholas J. Higham;Craig Lucas
Affiliations:
NAG Ltd., Oxford, England and School of Mathematics, University of Manchester, England;School of Mathematics, University of Manchester, England;Manchester Computing, University of Manchester, England
Venue:
PARA'06 Proceedings of the 8th international conference on Applied parallel computing: state of the art in scientific computing
Year:
2006

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Abstract

Routines exist in LAPACK for computing the Cholesky factorization of a symmetric positive definite matrix and in LINPACK there is a pivoted routine for positive semidefinite matrices. We present new higher level BLAS LAPACK-style codes for computing this pivoted factorization. We show that these can be many times faster than the LINPACK code. Also, with a new stopping criterion, there is more reliable rank detection and smaller normwise backward error. We also present algorithms that update the QR factorization of a matrix after it has had a block of rows or columns added or a block of columns deleted. This is achieved by updating the factors Q and R of the original matrix. We present some LAPACK-style codes and show these can be much faster than computing the factorization from scratch.