Backward error bounds for constrained least squares problems
An upper bound on the normwise backward error of an approximate solution to the equality constrained least squares problem is given. This is an attempt to answer to the question ``How much perturbations have to be registered, in order to obtain a sufficiently good approximate solution?''. Summarizing normwise backward error results for a linear system and for the least squares minimization over a sphere, upper and lower bounds for the backward errors are derived. Also some results, obtained from numerical experiments are given, to illustrate the practical effectiveness of the proposed way to reduce the size of the upper bound.
equality constrained least squares problem
scientific article; zbMATH DE number 1309450