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Applicable Analysis
An International Journal
Volume 89, 2010 - Issue 11: Regularization Theory and Applications
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Original Articles

Improved and extended results for enhanced convergence rates of Tikhonov regularization in Banach spaces

Andreas Neubauer Industrial Mathematics Institute, Johannes Kepler University Linz, A-4040 Linz, AustriaCorrespondence[email protected]
,
Torsten Hein Department of Mathematics, Chemnitz University of Technology, D-09107 Chemnitz, Germany
,
Bernd Hofmann Department of Mathematics, Chemnitz University of Technology, D-09107 Chemnitz, Germany
,
Stefan Kindermann Industrial Mathematics Institute, Johannes Kepler University Linz, A-4040 Linz, Austria
&
Ulrich Tautenhahn Department of Mathematics, University of Applied Sciences, Zittau/Görlitz, P.O.Box 1454, D-02754 Zittau, Germany
Pages 1729-1743 | Received 28 Sep 2009, Accepted 16 Nov 2009, Published online: 24 May 2010

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Zhenwu Fu, Yong Chen & Bo Han. (2022) REGINN-IT method with general convex penalty terms for nonlinear inverse problems. Applicable Analysis 101:17, pages 5949-5973.
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Baasansuren Jadamba, Akhtar A. Khan, Michael Richards, Miguel Sama & Christiane Tammer. (2020) Analyzing the role of the Inf-Sup condition for parameter identification in saddle point problems with application in elasticity imaging. Optimization 69:12, pages 2577-2610.
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Markus Grasmair. (2020) Source Conditions for Non-Quadratic Tikhonov Regularization. Numerical Functional Analysis and Optimization 41:11, pages 1352-1372.
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Christian Clason, Akhtar A. Khan, Miguel Sama & Christiane Tammer. (2019) Contingent derivatives and regularization for noncoercive inverse problems. Optimization 68:7, pages 1337-1364.
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Ying Wang, Jing Li & Jinping Wang. (2018) A convergence analysis of an inexact Newton-Landweber iteration method for nonlinear problem. Applicable Analysis 97:7, pages 1106-1116.
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Baasansuren Jadamba, Akhtar A. Khan, Miguel Sama & Christiane Tammer. (2017) On convex modified output least-squares for elliptic inverse problems: stability, regularization, applications, and numerics. Optimization 66:6, pages 983-1012.
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Natalia M. Yaparova. (2016) Mathematical modelling and method for solving a parametric identification problem for self-test of measuring devices. Inverse Problems in Science and Engineering 24:1, pages 77-91.
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Jens Flemming. (2012) Solution smoothness of ill-posed equations in Hilbert spaces: four concepts and their cross connections. Applicable Analysis 91:5, pages 1029-1044.
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Articles from other publishers (23)

Pallavi Mahale & Farheen M. Shaikh. (2023) Simplified REGINN-IT method in Banach spaces for nonlinear ill-posed operator equations. Journal of Inverse and Ill-posed Problems 0:0.
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Guangyu Gao, Bo HanZhenwu Fu & Shanshan Tong. (2023) A Fast Data-Driven Iteratively Regularized Method with Convex Penalty for Solving Ill-Posed Problems. SIAM Journal on Imaging Sciences 16:2, pages 640-670.
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Zhenwu Fu, Bo Han & Yong Chen. (2022) Levenberg–Marquardt method with general convex penalty for nonlinear inverse problems. Journal of Computational and Applied Mathematics 404, pages 113771.
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Baasansuren Jadamba, Akhtar A Khan, Michael Richards & Miguel Sama. (2020) A convex inversion framework for identifying parameters in saddle point problems with applications to inverse incompressible elasticity. Inverse Problems 36:7, pages 074003.
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Bernd Hofmann, Stefan Kindermann & Peter Mathé. (2019) Penalty-based smoothness conditions in convex variational regularization. Journal of Inverse and Ill-posed Problems 27:2, pages 283-300.
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Benjamin Sprung & Thorsten Hohage. (2018) Higher order convergence rates for Bregman iterated variational regularization of inverse problems. Numerische Mathematik 141:1, pages 215-252.
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Ge Guo, Guowei Tong, Lian Lu & Shi Liu. (2018) Iterative reconstruction algorithm for the inverse problems in electrical capacitance tomography. Flow Measurement and Instrumentation 64, pages 204-212.
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M. Cho, A. A. Khan, T. Malysheva, M. Sama & L. White. 2018. Applications of Nonlinear Analysis. Applications of Nonlinear Analysis 61 100 .
Liang Ding, Hui Zhao & Yixin Dou. (2017) Sparse Signal Inversion with Impulsive Noise by Dual Spectral Projected Gradient Method. Mathematical Problems in Engineering 2017, pages 1-17.
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Ivan Tomba & Barbara Kaltenbacher. (2015) Enhanced choice of the parameters in an iteratively regularized Newton-Landweber iteration in Banach space. Enhanced choice of the parameters in an iteratively regularized Newton-Landweber iteration in Banach space.
Bernd Hofmann. 2015. Mathematical and Computational Modeling. Mathematical and Computational Modeling 192 221 .
Jin Cheng & Bernd Hofmann. 2015. Handbook of Mathematical Methods in Imaging. Handbook of Mathematical Methods in Imaging 91 123 .
B. Jadamba, A. A. Khan, G. Rus, M. Sama & B. Winkler. (2014) A New Convex Inversion Framework for Parameter Identification in Saddle Point Problems with an Application to the Elasticity Imaging Inverse Problem of Predicting Tumor Location. SIAM Journal on Applied Mathematics 74:5, pages 1486-1510.
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Jin Cheng & Bernd Hofmann. 2020. Handbook of Mathematical Methods in Imaging. Handbook of Mathematical Methods in Imaging 1 31 .
Barbara Kaltenbacher & Ivan Tomba. (2013) Convergence rates for an iteratively regularized Newton–Landweber iteration in Banach space. Inverse Problems 29:2, pages 025010.
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Kristian Bredies & Mariya Zhariy. (2013) A discrepancy-based parameter adaptation and stopping rule for minimization algorithms aiming at Tikhonov-type regularization. Inverse Problems 29:2, pages 025008.
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Barbara Kaltenbacher. 2013. System Modeling and Optimization. System Modeling and Optimization 38 48 .
Bernd Hofmann & Peter Mathé. (2012) Parameter choice in Banach space regularization under variational inequalities. Inverse Problems 28:10, pages 104006.
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Alexandra Smirnova. (2012) On convergence rates for iteratively regularized procedures with linear penalty terms. Inverse Problems 28:8, pages 085005.
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Qinian Jin. (2012) Inexact Newton–Landweber iteration for solving nonlinear inverse problems in Banach spaces. Inverse Problems 28:6, pages 065002.
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Jin Cheng & Bernd Hofmann. 2011. Handbook of Mathematical Methods in Imaging. Handbook of Mathematical Methods in Imaging 87 109 .
Radu Ioan Boţ & Bernd Hofmann. (2010) An extension of the variational inequality approach for obtaining convergence rates in regularization of nonlinear ill-posed problems. Journal of Integral Equations and Applications 22:3.
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Jens Flemming. (2010) Theory and examples of variational regularization with non-metric fitting functionals. Journal of Inverse and Ill-posed Problems 18:6.
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