A new \(L\)-curve for ill-posed problems

DOI10.1016/j.cam.2007.01.025zbMath1145.65035OpenAlexW2037893344MaRDI QIDQ935810

Hassane Sadok, Lothar Reichel

Publication date: 8 August 2008

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2007.01.025

zbMATH Keywords

Fredholm integral equationnumerical examplesHilbert spacelinear operator equationtruncated singular value decomposition\(L\)-curvecompact linear operatorlinear ill-posed problemtruncation criteriontruncation index

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Numerical solutions to equations with linear operators (65J10) Equations and inequalities involving linear operators, with vector unknowns (47A50) Fredholm integral equations (45B05) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20)

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Uses Software

• Regularization tools
• corner.m

Cites Work

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• Extrapolation techniques for ill-conditioned linear systems
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• Multi-parameter regularization techniques for ill-conditioned linear systems
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• Iterative methods for ill-posed problems and semiconvergent sequences
• An adaptive pruning algorithm for the discrete L-curve criterion
• Improvement of the resolution of an instrument by numerical solution of an integral equation
• Remarks on choosing a regularization parameter using the quasi-optimality and ratio criterion
• A Technique for the Numerical Solution of Certain Integral Equations of the First Kind
• Analysis of Discrete Ill-Posed Problems by Means of the L-Curve
• The Use of the L-Curve in the Regularization of Discrete Ill-Posed Problems