Stability analysis of the method of seminormal equations for linear least squares problems

AbstractConsider the linear least squares problem minx‖Ax−b‖2. When A is large and sparse, then often only the R-factor in the QR factorization of A is known.The solution x can then be computed from the seminormal equations RTRx = ATb. For this method the error in x is shown to be of the same order as for the method of normal equations. We show that by adding a correction step using only single precision we get a method which under mild conditions is as accurate as the QR method. The application of this method to the updating of a sparse R-factor of A when appending a column is discussed