Hansen, Per Christian3; Jensen, Toke Koldborg4; Rodriguez, Giuseppe5
1 Scientific Computing, Department of Informatics and Mathematical Modeling, Technical University of Denmark2 Department of Informatics and Mathematical Modeling, Technical University of Denmark3 Department of Applied Mathematics and Computer Science, Technical University of Denmark4 National Institute of Aquatic Resources, Technical University of Denmark5 unknown
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.
Journal of Computational and Applied Mathematics, 2007, Vol 198, Issue 2, p. 483-492