An Adaptive Pruning Algorithm for the Discrete L-Curve Criterion |
Per Christian Hansen, Toke Koldborg Jensen, Giuseppe Rodriguez
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| Abstract | We describe a robust and adaptive implementation of the L-curve criterion, i.e., for locating the corner of a discrete L-curve consisting of a log-log plot of corresponding residual and solution norms of regularized solutions from a method with a discrete regularization parameter (such as truncated SVD or regularizing CG iterations). Our algorithm needs no pre-defined parameters, and in order to capture the global features of the curve in an adaptive fashion, we use a sequence of pruned L-curves that correspond to considering the curves at different scales. We compare our new algorithm to existing algoritms and demonstrate its robustness by numerical examples. |
| Keywords | Discrete ill-posed problems, L-curve criterion, regularization, parameter-choice method. |
| Type | Technical report |
| Year | 2004 |
| Publisher | Informatics and Mathematical Modelling, Technical University of Denmark, DTU |
| Address | Richard Petersens Plads, Building 321, DK-2800 Kgs. Lyngby |
| Series | IMM-Technical Report-2004-18 |
| Note | This work was supported in part by grant no. 21-03-0574 from the Danish Natural Science Research Foundation, and by COFIN grant no. 2002014121 from MIUR (Italy) |
| Electronic version(s) | [pdf] [ps] |
| BibTeX data | [bibtex] |
| IMM Group(s) | Scientific Computing |