Geodesic
Regularization parameter selection in discrete ill-posed problems—The use of the U-curve
International Journal of Applied Mathematics and Computer Science, Tome 17 (2007) no. 2, pp. 157-164.

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To obtain smooth solutions to ill-posed problems, the standard Tikhonov regularization method is most often used. For the practical choice of the regularization parameter we can then employ the well-known L-curve criterion, based on the L-curve which is a plot of the norm of the regularized solution versus the norm of the corresponding residual for all valid regularization parameters. This paper proposes a new criterion for choosing the regularization parameter , based on the so-called U-curve. A comparison of the two methods made on numerical examples is additionally included.
Keywords: ill-posed problems, Tikhonov regularization, regularization parameter, L-curve, U-curve
Mots-clés : problem niewłaściwie postawiony, regularyzacja Tichonowa, parametr regularyzacji 
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Krawczyk-Stańdo, D.; Rudnicki, M. Regularization parameter selection in discrete ill-posed problems—The use of the U-curve. International Journal of Applied Mathematics and Computer Science, Tome 17 (2007) no. 2, pp. 157-164. https://geodesic-test.mathdoc.fr/item/IJAMCS_2007_17_2_a1/

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