A Note on Iterative Refinement for Seminormal Equations

Abstrakt

We present a roundoff error analysis of the method for solving the linear least squares problems with full column rank matrix using only the diagonal and right orthogonal factors from the SVD decomposition of the system matrix. This method is an analogue of the method of seminormal equations, where the solution is computed using only the triangular factor fom the QR factorization of A. We analyze one step of fixed precision iterative refinement to improve the accuracy of this method a we show that under certain conditions, it produces a forward stable solution. However, it is generally not forward stable and has similar numerical properties to the corrected method of seminormal equations. We illustrate our analysis by numerical experiments.