AbstractA general analysis of the condition of the linear least squares problem is given. The influence of rounding errors is studied in detail for a modified version of the Gram-Schmidt… Expand

Iterative methods are developed for computing the Moore-Penrose pseudoinverse solution of a linear systemAx=b, whereA is anm ×n sparse matrix. The methods do not require the explicit formation ofATA… Expand

This paper arose from a fascinating observation, apparently by Charles Sheffield, and relayed to us by Gene Golub, that the QR factorization of an $m \times n$ matrix A via the modified Gram-Schmidt algorithm (MGS) is numerically equivalent to that arising from Householder transformations applied to the matrix A augmented by an n by n zero matrix.Expand

We obtain in this paper a considerable improvement over a method developed earlier by Ballester and Pereyra for the solution of systems of linear equations with Vandermonde matrices of coefficients.… Expand

Abstract A fast and stable method for computing the square root X of a given matrix A ( X 2 = A ) is developed. The method is based on the Schur factorization A = QSQ H and uses a fast recursion to… Expand