PERTURBATION-THEORY FOR THE RANK-DEFICIENT EQUALITY CONSTRAINED LEAST-SQUARES PROBLEM

This paper presents perturbation theory for the equality constrained least squares problem min f is-an-element-of S \\Kf - g\\2 with S = {f : \\Lf - h\\2 = min(y is-an-element of Cn) \\Ly - h \\2} (LSE), in which L and (L/K) may not be of full rank. The analysis generalizes the results of Elden [4]. Perturbation theorems for the LSE problem are proved. Numerical experiments are also given to verify the error bounds.