Volume 53, pp. 217-238, 2020.

A simplified L-curve method as error estimator

Stefan Kindermann and Kemal Raik


The L-curve method is a well known heuristic method for choosing the regularization parameter for ill-posed problems by selecting it according to the maximal curvature of the L-curve. In this article, we propose a simplified version that replaces the curvature essentially by the derivative of the parameterization on the $y$-axis. This method shows a similar behaviour to the original L-curve method, but unlike the latter, it may serve as an error estimator under typical conditions. Thus, we can accordingly prove convergence for the simplified L-curve method.

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Key words

heuristic parameter choice, L-curve method, regularization

AMS subject classifications

47A52, 65F22, 65J20, 65J22

Links to the cited ETNA articles

[20]Vol. 38 (2011), pp. 233-257 Stefan Kindermann: Convergence analysis of minimization-based noise level-free parameter choice rules for linear ill-posed problems
[21]Vol. 40 (2013), pp. 58-81 Stefan Kindermann: Discretization independent convergence rates for noise level-free parameter choice rules for the regularization of ill-conditioned problems

ETNA articles which cite this article

Vol. 57 (2022), pp. 216-241 Simon Hubmer, Ekaterina Sherina, Stefan Kindermann, and Kemal Raik: A numerical comparison of some heuristic stopping rules for nonlinear Landweber iteration
Vol. 58 (2023), pp. 348-377 Alessandro Buccini, Lucas Onisk, and Lothar Reichel: Range restricted iterative methods for linear discrete ill-posed problems

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