Non-convergence of the L-curve regularization parameter selection method
- 1 August 1996
- journal article
- Published by IOP Publishing in Inverse Problems
- Vol. 12 (4) , 535-547
- https://doi.org/10.1088/0266-5611/12/4/013
Abstract
The L-curve method was developed for the selection of regularization parameters in the solution of discrete systems obtained from ill-posed problems. An analysis of this method is given for selecting a parameter for Tikhonov regularization. This analysis, which is carried out in a semi-discrete, semi-stochastic setting, shows that the L-curve approach yields regularized solutions which fail to converge for a certain class of problems. A numerical example is also presented which indicates that this lack of convergence can arise in practical applications.Keywords
This publication has 9 references indexed in Scilit:
- Using the L--curve for determining optimal regularization parametersNumerische Mathematik, 1994
- The Use of the L-Curve in the Regularization of Discrete Ill-Posed ProblemsSIAM Journal on Scientific Computing, 1993
- Analysis of Discrete Ill-Posed Problems by Means of the L-CurveSIAM Review, 1992
- Asymptotic theory of filtering for linear operator equations with discrete noisy dataMathematics of Computation, 1987
- Optimal Choice of a Truncation Level for the Truncated SVD Solution of Linear First Kind Integral Equations When Data are NoisySIAM Journal on Numerical Analysis, 1986
- Practical Approximate Solutions to Linear Operator Equations When the Data are NoisySIAM Journal on Numerical Analysis, 1977
- Convergence rates of approximate least squares solutions of linear integral and operator equations of the first kindMathematics of Computation, 1974
- Well-posed stochastic extensions of ill-posed linear problemsJournal of Mathematical Analysis and Applications, 1970
- The error principle in the solution of operational equations by the regularization methodUSSR Computational Mathematics and Mathematical Physics, 1968