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. © 2000 Elsevier Science B.V.

Calvetti, D., Morigi, S., Reichel, L., Sgallari, F. (2000). Tikhonov regularization and the L-curve for large discrete ill-posed problems. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 123(1-2), 423-446 [10.1016/S0377-0427(00)00414-3].

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

Morigi S.;Reichel L.;Sgallari F.
2000

Abstract

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. © 2000 Elsevier Science B.V.
2000
Calvetti, D., Morigi, S., Reichel, L., Sgallari, F. (2000). Tikhonov regularization and the L-curve for large discrete ill-posed problems. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 123(1-2), 423-446 [10.1016/S0377-0427(00)00414-3].
Calvetti, D.; Morigi, S.; Reichel, L.; Sgallari, F.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/879661
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