Parallel QR Decomposition of a rectangular matrix

A new algorithm for downdating a QR decomposition is presented. We show that, when the columns in the Q factor from the Modified Gram-Schmidt QR decomposition of a matrixX are exactly orthonormal, the Gram-Schmidt downdating algorithm for the QR ...

Let A be an $m \times n$ matrix of rank n. The $QR$ factorization of A decomposes A into the product of an $m \times n$ matrix Q with orthonormal columns and a nonsingular upper triangular matrix R. The decomposition is essentially unique, Q being ...

Solutions to rank deficient least squares problems are conveniently expressed in terms of the singular value decomposition (SVD) of the coefficient matrix. When the matrix is nearly rank deficient, a common procedure is to neglect its smallest singular ...