Comparison of the method of averages with the method of least squares.

Abstract

It is shown that the computationally simple method of averages can yield a surprisingly good solution of an overdetermined system of linear equations, provided that the grouping of the equations is done in an appropriate way. The notion of angle between linear subspaces is applied in a general comparison of this method and the method of least squares. The optimal application of the method is treated for the test problem of fitting a polynomial of degree less than six.