Abstract

. It is shown that the basic regularization procedures for finding meaningful approximate solutions of ill-conditioned or singular linear systems can be phrased and analyzed in terms of classical linear algebra that can be taught in any numerical analysis course. Apart from rewriting many known results in a more elegant form, we also derive a new two-parameter family of merit functions for the determination of the regularization parameter. The traditional merit functions from generalized cross validation (GCV) and generalized maximum likelihood (GML) are recovered as special cases. Key words. regularization, ill-posed, ill-conditioned, generalized cross validation, generalized maximum likelihood, Tikhonov regularization, error bounds AMS subject classifications. primary 65F05; secondary 65J20 1. Introduction. In many applications of linear algebra, the need arises to find a good approximation x to a vector x 2 IR n satisfying an approximate equation Ax ß y with ill-conditioned o...

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