QR factorization with complete pivoting and accurate computation of the SVD

Umist Qr Factorization with Complete Pivoting and Accurate Computation of the Svd Departments of Mathematics

QR factorization with complete pivoting and accurate computation of the SVD

A new algorithm of Demmel et al. for computing the singular value decomposition (SVD) to high relative accuracy begins by computing a rank-revealing decomposition (RRD). Demmel et al. analyse the use of Gaussian elimination with complete pivoting (GECP) for computing the RRD. We investigate the use of QR factorization with complete pivoting (that is, column pivoting together with row sorting or...

QR Factorization with Complete Pivotingand Accurate Computation of the SVDNicholas

Householder QR Factorization With Randomization for Column Pivoting (HQRRP)

A fundamental problem when adding column pivoting to the Householder QR factorization is that only about half of the computation can be cast in terms of high performing matrixmatrix multiplications, which greatly limits the benefits that can be derived from so-called blocking of algorithms. This paper describes a technique for selecting groups of pivot vectors by means of randomized projections...

Communication Avoiding Rank Revealing QR Factorization with Column Pivoting

In this paper we introduce CARRQR, a communication avoiding rank revealing QRfactorization with tournament pivoting. We show that CARRQR reveals the numerical rank of amatrix in an analogous way to QR factorization with column pivoting (QRCP). Although the upperbound of a quantity involved in the characterization of a rank revealing factorization is worse forCARRQR than for QRCP...