An Elimination Method for the Solution of Linear Least Squares Problems

An elimination method for solving the linear least squares problem is presented which can be considered a generalization of the Gaussian elimination method for square, linear systems. Operations counts are given indicating the greater efficiency of this method over all known methods (including the fast but poorly conditioned normal equations approach) when the systems are slightly overdetermined (i.e., the number of equations is nearly the number of unknowns). An extension of this method is given for the solution of the minimal least squares problem associated with rank deficient systems of equations.