The perturbation analysis of weighted and constrained rank-deficient linear
least squares is difficult without the use of the augmented system of equa
tions. In this paper a general form of the augmented system is used to get
simple perturbation identities and perturbation bounds for the general line
ar least squares problem both for the full-rank and rank-deficient problem.
Perturbation identities for the rank-deficient weighted and constrained ca
se are found as a special case. Interesting perturbation bounds and conditi
on 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.