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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
