On the stability of the direct elimination method for equality constrained least squares problems (Q1577401)

Numerical stability of the direct elimination method for linear equality constrained least squares problems is studied following Wilkinson's backward error analysis approach. To this end the original problem is reduced to a lower-dimensional unconstrained least squares problem using constraints to eliminate variables. It is shown that the solution computed by the method is the exact solution of a perturbed problem and bounds for data perturbations are given. The developed analysis indicates the dependence of the numerical stability of the method on the way in which constraints are used to eliminate variables. Numerical experience with the method represented confirms the theoretical considerations.