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

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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. https://doi.org/10.1016/S0377-0427(00)00414-3

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