Tikhonov regularization and the L-curve for large discrete ill-posed problems

Discretization of linear inverse problems generally gives rise to very ill-conditioned linear systems of algebraic equations. Typically, the linear systems obtained have to be regularized to make the computation of a meaningful approximate solution possible. Tikhonov regularization is one of the mos...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2000-11, Vol.123 (1), p.423-446
Main Authors: Calvetti, D., Morigi, S., Reichel, L., Sgallari, F.
Format: Article
Language:English
Subjects:
Gauss quadrature
Ill-posed problem
L-curve criterion
Regularization
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Summary:Discretization of linear inverse problems generally gives rise to very ill-conditioned linear systems of algebraic equations. Typically, the linear systems obtained have to be regularized to make the computation of a meaningful approximate solution possible. Tikhonov regularization is one of the most popular regularization methods. A regularization parameter specifies the amount of regularization and, in general, an appropriate value of this parameter is not known a priori. We review available iterative methods, and present new ones, for the determination of a suitable value of the regularization parameter by the L-curve criterion and the solution of regularized systems of algebraic equations.
ISSN:0377-0427
1879-1778
DOI:10.1016/S0377-0427(00)00414-3