Stability of the solutions of linear least squares problems

SummaryIn 1966 Golub and Wilkinson gave upper bounds for the errors of least squares solutions based on orthogonal transformations, in which the square of the condition number of the matrix occurs. In the present paper a geometrical explanation and lower bounds are given. The upper bounds will be shown to be realistic for some classes of problems and types of perturbations, and to be unrealistic for others.