Solving ill-conditioned and singular linear systems: A tutorial on regularization

Arnold Neumaier

doi:10.1137/S0036144597321909

1998-01-01

501

PRE

Arnold Neumaier

DOI：10.1137/S0036144597321909

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摘要

En 中文

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.

Keyword:

regularization

ill-posed

ill-conditioned

generalized cross validation

generalized maximum likelihood

Tikhonov regularization

error bounds

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期刊

SIAM Review

IF:

6.1

论文数:

888

被引数:

1.2W

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