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A new variant of L-curve for Tikhonov regularization

Mansoor Rezghi, S. Mohammad Hosseini
2009 Journal of Computational and Applied Mathematics  
In this paper we introduce a new variant of L-curve to estimate the Tikhonov regularization parameter for the regularization of discrete ill-posed problems.  ...  This method uses the solution norm versus the regularization parameter. The numerical efficiency of this new method is also discussed by considering some test problems.  ...  for Tikhonov regularization.  ... 
doi:10.1016/ fatcat:5ggdbmzaujgfbdi5ugadik6kem

Regularization with randomized SVD for large-scale discrete inverse problems

Hua Xiang, Jun Zou
2013 Inverse Problems  
A key issue for the success of the Tikhonov regularization is how to determine a reasonable regularization parameter µ.  ...  If there is a corner on the L-curve, one can take the corresponding parameter µ as the desired regularization parameter.  ...  Acknowledgments The authors would like to thank two anonymous referees and the board member for their numerous insightful and constructive comments.  ... 
doi:10.1088/0266-5611/29/8/085008 fatcat:n37ai5pzkbclvnfwhnuedzrtkm

Optimization of drug controlled release from multi-laminated devices based on the modified Tikhonov regularization method [article]

Xinming Zhang, Ling Ma
2019 arXiv   pre-print
In view of the ill-posedness of the corresponding inverse problem, a modified Tikhonov regularization method is proposed by constructing a new regularizing filter function based on the singular value theory  ...  The numerical results demonstrate that the modified Tikhonov regularization method not only has the optimal asymptotic order, but also is suitable for the optimization and design of multi-laminated drug  ...  The regularization parameter is chosen by using the L-curve method, and the corresponding curve is shown in Fig.2 and Fig.4.  ... 
arXiv:1904.05999v1 fatcat:n6lilkxsnfbdlpw6ti4stcxxum

Page 6922 of Mathematical Reviews Vol. , Issue 95k [page]

1995 Mathematical Reviews  
The L-curve strategy for choosing a, considered for Tikhonov regularization in finite-dimensional spaces by P. C.  ...  Finally, the authors show how L-curves can be used to compute the regularization parameters for Morozov’s discrepancy principle and also for a variant of it proposed by Gfrerer. L. J.  ... 

A Comparative Study of Regularization Method in Structure Load Identification

Bingrong Miao, Feng Zhou, Chuanying Jiang, Xiangyu Chen, Shuwang Yang
2018 Shock and Vibration  
The TSVD based on GCV method has more advantages than the Tikhonov based on L-curve method.  ...  The results show that using the two identification methods Tikhonov (L-curve) and TSVD (GCV-curve) can successfully and accurately identify the different excitation forces of the external hammer.  ...  Methods for Selecting the Tikhonov Regularization Parameter 4.1. L-Curve Criterion.  ... 
doi:10.1155/2018/9204865 fatcat:dlzd5xmwn5gthat5mmgtvfq7w4

A new regularization method for linear exponentially ill-posed problems [article]

Walter Cedric Simo Tao Lee
2020 arXiv   pre-print
This paper provides a new regularization method which is particularly suitable for linear exponentially ill-posed problems.  ...  Finally, numerical experiments on three test problems attest the better performance of the new method compared to the well known Tikhonov method in instances of exponentially ill-posed problems.  ...  Acknowledgements: The author would like to thank Pierre Maréchal, Anne Vanhems for their helpful comments, readings and remarks.  ... 
arXiv:1909.12020v2 fatcat:msb3ap3z5nbxzo7kac5fsjqe44

Global Mapping of an Exo-Earth using Sparse Modeling [article]

Masataka Aizawa, Hajime Kawahara, Siteng Fan
2020 arXiv   pre-print
We develop a new retrieval scheme for obtaining two-dimensional surface maps of exoplanets from scattered light curves.  ...  We apply the new method to simulated scattered light curves of the Earth, and find that the new method provides a better spatial resolution of the reconstructed map than those using Tikhonov regularization  ...  and the new regularization.  ... 
arXiv:2004.03941v2 fatcat:tjbgxu26ynfojpqdaa6n7ny4om

An improved fixed-point algorithm for determining a Tikhonov regularization parameter

Fermín S Viloche Bazán, Juliano B Francisco
2009 Inverse Problems  
The method determines a Tikhonov parameter associated with a point near the L-corner of the maximum curvature and at which the L-curve is locally convex.  ...  We derive a simple and computable condition which describes the regions where the L-curve is concave/convex, while providing insight into the choice of the regularization parameter through the L-curve  ...  Acknowledgments The authors are indebted to the referees for their careful reading of this paper and for their constructive criticism that improved both the quality and the presentation of this work.  ... 
doi:10.1088/0266-5611/25/4/045007 fatcat:mga2ftk5rze3distscp43e6z4m

Residual periodograms for choosing regularization parameters for ill-posed problems

Bert W Rust, Dianne P O'Leary
2008 Inverse Problems  
We compare this method with standard techniques such as the discrepancy principle, the L-curve, and generalized cross validation, showing that it performs better on two new test problems as well as a variety  ...  We discuss methods for choosing a regularization parameter in order to assure that the residual for the model is statistically plausible.  ...  Vangel for suggestions for improving the statistical aspects of this manuscript. We are grateful to Drs. M.E. Kilmer and P.C. Hansen for sharing their software.  ... 
doi:10.1088/0266-5611/24/3/034005 fatcat:lk7lboym5nfbjp2bgir3btdici

A simplified L-curve method as error estimator

Stefan Kindermann, Kemal Raik
2020 Electronic Transactions on Numerical Analysis  
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.  ...  Thus, we can accordingly prove convergence for the simplified L-curve method.  ...  We would like to thank the anonymous referees for their useful comments.  ... 
doi:10.1553/etna_vol53s217 fatcat:x3kw424mjrblnn4acryjx4x4ja

A simplified L-curve method as error estimator [article]

Stefan Kindermann, Kemal Raik
2019 arXiv   pre-print
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.  ...  Thus, we can accordingly prove convergence for the simplified L-curve method.  ...  The L-curve The L-curve is a plot of the (logarithm of the) residual against the (logarithm of the) norm of the regularized solution.  ... 
arXiv:1908.10140v1 fatcat:2hrs7l5gg5bxbdduqztyxwuhuq

Optimal Tikhonov regularization for DEER spectroscopy

Thomas H. Edwards, Stefan Stoll
2018 Journal of magnetic resonance (San Diego, Calif. 1997 : Print)  
This method requires the selection of a regularization parameter, α, and a regularization operator, L.  ...  They perform significantly better than currently utilized L-curve methods.  ...  A thorough paper examining Tikhonov regularization and introducing the use of the L-curve maximumcurvature criterion appeared in 2005 [6] .  ... 
doi:10.1016/j.jmr.2018.01.021 pmid:29414064 pmcid:PMC5840305 fatcat:wphtxg5b2zaszpz74kjixeyggm

Automatic parameter setting for Arnoldi–Tikhonov methods

Silvia Gazzola, Paolo Novati
2014 Journal of Computational and Applied Mathematics  
In the framework of iterative regularization techniques for large-scale linear ill-posed problems, this paper introduces a novel algorithm for the choice of the regularization parameter when performing  ...  Assuming that we can apply the discrepancy principle, this new strategy can work without restrictions on the choice of the regularization matrix.  ...  We remark that a variant of this method, the so called Range Restricted Arnoldi-Tikhonov (RRAT) method, has been proposed in [10] .  ... 
doi:10.1016/ fatcat:waaetw2vgbbbhna5tjqo5r6xzq

REGULARIZATION TOOLS: A Matlab package for analysis and solution of discrete ill-posed problems

Per Christian Hansen
1994 Numerical Algorithms  
I am indebted to the many users of Regularization Tools who have provided criticism, feedback and suggestions to the package since its release!  ...  A consequence of this is that one can compare other regularization methods with Tikhonov regularization by inspecting how close the L-curve for the alternative method is to the Tikhonov L-curve.  ...  We note in passing that the L-curve is a continuous curve when the regularization parameter is continuous as in Tikhonov regularization.  ... 
doi:10.1007/bf02149761 fatcat:3ahktwjvmrayxpjdmh5y4pobua

SVD-tail: a new linear-sampling reconstruction method for inverse scattering problems

M'Barek Fares, Serge Gratton, Philippe L Toint
2009 Inverse Problems  
At variance with previously published techniques where the solution is constructed as a regularized solution of the far-field equations using a variant of the Tikhonov-Morozov type, the new method uses  ...  A new numerical procedure (SVD-tail) is proposed for the reconstruction of the shape and volume of unknown objects from measurements of their radiation in the far field.  ...  (Centre Interuniversitaire de Calcul de Toulouse) for providing access to the Grid'MIP machine for producing the synthtic data.  ... 
doi:10.1088/0266-5611/25/9/095013 fatcat:zgnsq5eizje5xpkdj6u6b3isqa
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