engleski

On the Failure of Rank Revealing QR Factorization Software

The QR factorization of matrix A using the Businger-Golub pivoting (AP = QR) is a core procedure in many solvers in numerical linear algebra, such as one-sided Jacobi SVD algorithm or linear least squares problem solver. A failure of producing P, Q and R with required properties may lead to failure of such more complex solvers. We report and analyze a problem in widely used LAPACK routines xGEQPF and xGEQP3 which implement this QR factorization. These routines may compute a triangular factor R whose structure dramatically differs from the required one in Businger-Golub pivot strategy. We propose a solution to the subtle numerical bug in this software. This solution has been included in the most recent version of LAPACK (3.1.0).

numerical software; QR factorization; pivoting; LAPACK

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