On the Stability of the Direct Elimination Method for Equality Constrained Least Squares Problems

摘要

A backward error analysis ofthe direct elimination method for linearequality constrained least squares problems is presented. It is proved that the solution computed by the method is the exact solution of a pertutbedproblem and bounds for data perturbations are given. The numerical stability of the method is related tothe way in which the constraints areused toeliminate variables and these theoretical conclusions are confirmedby a numerical example.