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Solving ill-conditioned and singular linear systems: A tutorial on regularization
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DOI：10.1137/S0036144597321909.png)
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Abstract
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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 elementary 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.
Keywords:
regularization
ill-posed
ill-conditioned
generalized cross validation
generalized maximum likelihood
Tikhonov regularization
error bounds
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Meeting report from the fourth meeting of the Computational Modeling in Biology Network (COMBINE)
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