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Numerical Functional Analysis and Optimization Volume 30, 2009 - Issue 9-10: NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION TRIBUTE TO GENNADI VAINIKKO
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Original Articles

On Minimization Strategies for Choice of the Regularization Parameter in Ill-Posed Problems

U. Hämarik Institute of Mathematics, Faculty of Mathematics and Computer Sciences, University of Tartu, Tartu, EstoniaCorrespondence[email protected]
,
R. Palm Institute of Computer Science, Faculty of Mathematics and Computer Sciences, University of Tartu, Tartu, Estonia
&
T. Raus Institute of Mathematics, Faculty of Mathematics and Computer Sciences, University of Tartu, Tartu, Estonia
Pages 924-950 | Received 01 Jul 2009, Accepted 24 Aug 2009, Published online: 22 Dec 2009

Citations (20)

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Read on this site (3)

Marek Andrzej Kojdecki. (2014) Heuristic two-parameter regularization based on second discrepancy principle for Tikhonov’s method. Inverse Problems in Science and Engineering 22:2, pages 282-296.
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Uno Hämarik, Urve Kangro, Reimo Palm, Toomas Raus & Ulrich Tautenhahn. (2014) Monotonicity of error of regularized solution and its use for parameter choice. Inverse Problems in Science and Engineering 22:1, pages 10-30.
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Kazufumi Ito, Bangti Jin & Jun Zou. (2011) A new choice rule for regularization parameters in Tikhonov regularization. Applicable Analysis 90:10, pages 1521-1544.
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Articles from other publishers (17)

Oleg Matysik & Marc M. Van Hulle. (2022) Alternating step size method for solving ill-posed linear operator equations in energetic space. Journal of Computational and Applied Mathematics 416, pages 114553.
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Toomas Raus & Uno Hämarik. (2020) Q-Curve and Area Rules for Choosing Heuristic Parameter in Tikhonov Regularization. Mathematics 8:7, pages 1166.
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Federico Benvenuto & Bangti Jin. (2020) A parameter choice rule for Tikhonov regularization based on predictive risk. Inverse Problems 36:6, pages 065004.
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Rosemary A. Renaut, Anthony W. Helmstetter & Saeed Vatankhah. (2019) Unbiased predictive risk estimation of the Tikhonov regularization parameter: convergence with increasing rank approximations of the singular value decomposition. BIT Numerical Mathematics 59:4, pages 1031-1061.
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Federico Benvenuto & Cristina Campi. (2019) A discrepancy principle for the Landweber iteration based on risk minimization. Applied Mathematics Letters 96, pages 1-6.
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Uno Hämarik, Urve Kangro, Stefan Kindermann & Kemal Raik. (2019) Semi-heuristic parameter choice rules for Tikhonov regularisation with operator perturbations. Journal of Inverse and Ill-posed Problems 27:1, pages 117-131.
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Stefan Bosse, Dirk Lehmhus, Walter Lang & Matthias BusseArmin Lechleiter & Stefan Bosse. 2018. Material-Integrated Intelligent Systems - Technology and Applications. Material-Integrated Intelligent Systems - Technology and Applications 301 328 .
Mark S. Gockenbach & Elaheh Gorgin. (2018) On the Convergence of a Heuristic Parameter Choice Rule for Tikhonov Regularization. SIAM Journal on Scientific Computing 40:4, pages A2694-A2719.
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Toomas Raus & Uno Hämarik. 2018. New Trends in Parameter Identification for Mathematical Models. New Trends in Parameter Identification for Mathematical Models 227 244 .
G. Landi, E. Loli Piccolomini & I. Tomba. (2016) A stopping criterion for iterative regularization methods. Applied Numerical Mathematics 106, pages 53-68.
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Uno Hämarik. On comparison of accuracy of approximate solutions of operator equations with noisy data. On comparison of accuracy of approximate solutions of operator equations with noisy data.
Frank Bauer, Martin Gutting & Mark A. Lukas. 2015. Handbook of Geomathematics. Handbook of Geomathematics 1713 1774 .
Hua Xiang & Jun Zou. (2013) Regularization with randomized SVD for large-scale discrete inverse problems. Inverse Problems 29:8, pages 085008.
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Frank Bauer, Martin Gutting & Mark A. Lukas. 2020. Handbook of Geomathematics. Handbook of Geomathematics 1 55 .
Uno Hämarik, Reimo Palm & Toomas Raus. (2012) A family of rules for parameter choice in Tikhonov regularization of ill-posed problems with inexact noise level. Journal of Computational and Applied Mathematics 236:8, pages 2146-2157.
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Frank Bauer & Mark A. Lukas. (2011) Comparingparameter choice methods for regularization of ill-posed problems. Mathematics and Computers in Simulation 81:9, pages 1795-1841.
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Uno Hämarik, Reimo Palm & Toomas Raus. (2010) Comparison of parameter choices in regularization algorithms in case of different information about noise level. Calcolo 48:1, pages 47-59.
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