REGULARIZATION PARAMETER SELECTION IN DISCRETE ILL-POSED PROBLEMS - THE USE OF THE U-CURVE

摘要

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.