An Adaptive Pruning Algorithm for the Discrete LCurve Criterion 
Per Christian Hansen, Toke Koldborg Jensen, Giuseppe Rodriguez

Abstract  We describe a robust and adaptive implementation of the Lcurve criterion, i.e., for locating the corner of a discrete Lcurve consisting of a loglog 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 predefined parameters, and in order to capture the global features of the curve in an adaptive fashion, we use a sequence of pruned Lcurves 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 illposed problems, Lcurve criterion, regularization, parameterchoice method. 
Type  Technical report 
Year  2004 
Publisher  Informatics and Mathematical Modelling, Technical University of Denmark, DTU 
Address  Richard Petersens Plads, Building 321, DK2800 Kgs. Lyngby 
Series  IMMTechnical Report200418 
Note  This work was supported in part by grant no. 21030574 from the Danish Natural Science Research Foundation, and by COFIN grant no. 2002014121 from MIUR (Italy) 
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IMM Group(s)  Scientific Computing 