Perturbation theory for generalized and constrained linear least squares

The perturbation analysis of weighted and constrained rank-deficient linear least squares is difficult without the use of the augmented system of equations. In this paper a general form of the augmented system is used to get simple perturbation identities and perturbation bounds for the general linear least squares problem both for the full-rank and rank-deficient problem. Perturbation identities for the rank-deficient weighted and constrained case are found as a special case. Interesting perturbation bounds and condition numbers are derived that may be useful when considering the stability of a solution of the rank-deficient general least squares problem. Copyright (C) 2000 John Wiley & Sons, Ltd.