TABLE OF CONTENTS For some time it has been believed that orthogonalizing methods did not suffer this squaring of the condition number ... It caused something of a shock, therefore, when in 1966 Golub and Wilkinson ... asserted that already the multiplications QA and Qb may produce errors in the solution containing a factor ? 2( A).
- A. VAN DER SLUIS,
Stability of the Solutions of Linear Least Squares Problems (1975)
Most packaged regression problems do compute a cross-products matrix and solve the normal equations using a matrix inversion subroutine. All the programs ... that disagreed (and some of those that agreed) with the unperturbed solution tried to solve the normal equations.
- ALBERT E. BEATON, DONALD B. RUBIN, and JOHN L. BARONE,
The Acceptability of Regression Solutions: Another Look at Computational Accuracy (1976)
On January 1, 1801 Giuseppe Piazzi discovered the asteroid Ceres. Ceres was only visible for forty days before it was lost to view behind the sun ... Gauss, using three observations, extensive analysis, and the method of least squares, was able to determine the orbit with such accuracy that Ceres was easily found when it reappeared in late 1801.
- DAVID K. KAHANER, CLEVE B. MOLER, and STEPHEN G. NASH,
Numerical Methods and Software (1989)
In this chapter we consider the least squares (LS) problem min x b ? Ax 2, where 
has full rank. We begin by examining the sensitivity of the LS problem to perturbations. Then we...
