An adaptive pruning algorithm for the discrete L-curve criterion |
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Authors: | Per Christian Hansen Toke Koldborg Jensen Giuseppe Rodriguez |
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Affiliation: | 1. Informatics and Mathematical Modelling, Technical University of Denmark, Building 321, DK-2800 Lyngby, Denmark;2. Dipartimento di Matematica e Informatica, Università di Cagliari, viale Merello 92, I-09123 Cagliari, Italy |
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Abstract: | We describe a robust and adaptive implementation of the L-curve criterion. The algorithm locates the corner of a discrete L-curve which is a log–log plot of corresponding residual norms 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 predefined 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 algorithms and demonstrate its robustness by numerical examples. |
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Keywords: | Discrete ill-posed problems L-curve criterion Regularization Parameter-choice method |
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