On the perturbation of least squares problems with equality constraints

Abstract

Some new perturbation results are presented for least squares problems with equality constraints, in which relative errors are obtained on perturbed solutions, least squares residuals, and vectors of Lagrange multipliers of the problem, based on the equivalence of the problem to a usual least squares problem and optimal perturbation results for orthogonal projections.

Keywords:

• Least squares solution
• generalized inverses

AMS Subject Classification:

• 15A09
• 65F20