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An adaptive pruning algorithm for the discrete L-curve criterion. (English) Zbl 1101.65044
Summary: 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 singular value decomposition or regularizing conjugate gradient 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.

MSC:
65F22 Ill-posedness and regularization problems in numerical linear algebra
65F20 Numerical solutions to overdetermined systems, pseudoinverses
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