A Note on Deferred Correction for Equality Constrained Least Squares Problems
Jesse L. Barlow, Udaya B. Vemulapati · SIAM Journal on Numerical Analysis · 1992
The solution of the equality constrained least squares problem is considered $\min _{x \in R^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. Numer. 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.