SOLVING ILL-CONDITIONED AND SINGULAR LINEAR-SYSTEMS - A TUTORIAL ON REGULARIZATION

It is shown that the basic regularization procedures for finding meani ngful approximate solutions of ill-conditioned or singular linear syst ems can be phrased and analyzed in terms of classical linear algebra t hat can be taught in any numerical analysis course. Apart from rewriti ng many known results in a more elementary form, we also derive a new two-parameter family of merit functions for the determination of the r egularization parameter. The traditional merit functions from generali zed cross validation (GCV) and generalized maximum likelihood (GML) ar e recovered as special cases.