Note on deferred correction for equality constrained least squares problems

The solution of the equality constrained least squares problem is considered min_xcR(n) ∥f-Ex∥₂ subject to Cx=g is considered. It is shown that for well-conditioned or moderately ill-conditioned problems of this form, the deferred correction procedure of Van Loan [SIAM J. Number, Anal, 22 (1985), pp. 851-864] can be made to converge in two iterations. The implementation suggestions due to Barlow [SIAM J. Numer. Anal, 25 (1988), pp. 1340-1358] are modified to obtain a more robust strategy. This modification was discovered in numerical experiments to verify the quick convergence proven in this paper. The new implementation seems to always obtain the predicted convergence behavior.