A simplified L-curve method as error estimator
Stefan Kindermann, Kemal Raik
Abstract
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.
Topics & Concepts
EstimatorMathematicsCurvatureRegularization (linguistics)Convergence (economics)Applied mathematicsHeuristicMathematical optimizationError analysisAlgorithmMinificationDerivative (finance)Mean squared errorSecond derivativeNoisy dataEstimation theoryNumerical methods in inverse problemsOptimization and Variational AnalysisAdvanced Numerical Analysis Techniques