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 α 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 α, based on the so-called U-curve. A comparison of the two methods made on numerical examples is additionally included.
@article{bwmeta1.element.bwnjournal-article-amcv17i2p157bwm,
author = {Krawczyk-Sta\'ndo, Dorota and Rudnicki, Marek},
title = {Regularization parameter selection in discrete ill-posed problems - the use of the U-curve},
journal = {International Journal of Applied Mathematics and Computer Science},
volume = {17},
year = {2007},
pages = {157-164},
zbl = {1120.49032},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv17i2p157bwm}
}
Krawczyk-Stańdo, Dorota; Rudnicki, Marek. 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) pp. 157-164. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv17i2p157bwm/
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