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On Levenberg-Marquardt-Kaczmarz iterative methods for solving systems of nonlinear ill-posed equations
1. | Fachbereich Mathematik, Johann Wolfgang Goethe Universität, Robert–Mayer–Str. 6–10, 60054 Frankfurt am Main, Germany |
2. | University of Graz, Institute for Mathematics and Scientific Computing, Heinrichstr. 36/III, A-8010 Graz, Austria |
3. | Department of Mathematics, Federal University of St. Catarina, P.O. Box 476, 88040-900 Florianópolis, Brazil |
[1] |
Jinyan Fan, Jianyu Pan. Inexact Levenberg-Marquardt method for nonlinear equations. Discrete and Continuous Dynamical Systems - B, 2004, 4 (4) : 1223-1232. doi: 10.3934/dcdsb.2004.4.1223 |
[2] |
Markus Haltmeier, Richard Kowar, Antonio Leitão, Otmar Scherzer. Kaczmarz methods for regularizing nonlinear ill-posed equations II: Applications. Inverse Problems and Imaging, 2007, 1 (3) : 507-523. doi: 10.3934/ipi.2007.1.507 |
[3] |
Jinyan Fan, Jianyu Pan. On the convergence rate of the inexact Levenberg-Marquardt method. Journal of Industrial and Management Optimization, 2011, 7 (1) : 199-210. doi: 10.3934/jimo.2011.7.199 |
[4] |
Liyan Qi, Xiantao Xiao, Liwei Zhang. On the global convergence of a parameter-adjusting Levenberg-Marquardt method. Numerical Algebra, Control and Optimization, 2015, 5 (1) : 25-36. doi: 10.3934/naco.2015.5.25 |
[5] |
Markus Haltmeier, Antonio Leitão, Otmar Scherzer. Kaczmarz methods for regularizing nonlinear ill-posed equations I: convergence analysis. Inverse Problems and Imaging, 2007, 1 (2) : 289-298. doi: 10.3934/ipi.2007.1.289 |
[6] |
Jinyan Fan. On the Levenberg-Marquardt methods for convex constrained nonlinear equations. Journal of Industrial and Management Optimization, 2013, 9 (1) : 227-241. doi: 10.3934/jimo.2013.9.227 |
[7] |
Stefan Kindermann. Convergence of the gradient method for ill-posed problems. Inverse Problems and Imaging, 2017, 11 (4) : 703-720. doi: 10.3934/ipi.2017033 |
[8] |
Haiyan Wang, Jinyan Fan. Convergence properties of inexact Levenberg-Marquardt method under Hölderian local error bound. Journal of Industrial and Management Optimization, 2021, 17 (4) : 2265-2275. doi: 10.3934/jimo.2020068 |
[9] |
Xin-He Miao, Kai Yao, Ching-Yu Yang, Jein-Shan Chen. Levenberg-Marquardt method for absolute value equation associated with second-order cone. Numerical Algebra, Control and Optimization, 2022, 12 (1) : 47-61. doi: 10.3934/naco.2021050 |
[10] |
Paola Favati, Grazia Lotti, Ornella Menchi, Francesco Romani. An inner-outer regularizing method for ill-posed problems. Inverse Problems and Imaging, 2014, 8 (2) : 409-420. doi: 10.3934/ipi.2014.8.409 |
[11] |
Adriano De Cezaro, Johann Baumeister, Antonio Leitão. Modified iterated Tikhonov methods for solving systems of nonlinear ill-posed equations. Inverse Problems and Imaging, 2011, 5 (1) : 1-17. doi: 10.3934/ipi.2011.5.1 |
[12] |
Guozhi Dong, Bert Jüttler, Otmar Scherzer, Thomas Takacs. Convergence of Tikhonov regularization for solving ill-posed operator equations with solutions defined on surfaces. Inverse Problems and Imaging, 2017, 11 (2) : 221-246. doi: 10.3934/ipi.2017011 |
[13] |
Matthew A. Fury. Regularization for ill-posed inhomogeneous evolution problems in a Hilbert space. Conference Publications, 2013, 2013 (special) : 259-272. doi: 10.3934/proc.2013.2013.259 |
[14] |
Misha Perepelitsa. An ill-posed problem for the Navier-Stokes equations for compressible flows. Discrete and Continuous Dynamical Systems, 2010, 26 (2) : 609-623. doi: 10.3934/dcds.2010.26.609 |
[15] |
Zonghao Li, Caibin Zeng. Center manifolds for ill-posed stochastic evolution equations. Discrete and Continuous Dynamical Systems - B, 2022, 27 (5) : 2483-2499. doi: 10.3934/dcdsb.2021142 |
[16] |
Felix Lucka, Katharina Proksch, Christoph Brune, Nicolai Bissantz, Martin Burger, Holger Dette, Frank Wübbeling. Risk estimators for choosing regularization parameters in ill-posed problems - properties and limitations. Inverse Problems and Imaging, 2018, 12 (5) : 1121-1155. doi: 10.3934/ipi.2018047 |
[17] |
Ye Zhang, Bernd Hofmann. Two new non-negativity preserving iterative regularization methods for ill-posed inverse problems. Inverse Problems and Imaging, 2021, 15 (2) : 229-256. doi: 10.3934/ipi.2020062 |
[18] |
Lianwang Deng. Local integral manifolds for nonautonomous and ill-posed equations with sectorially dichotomous operator. Communications on Pure and Applied Analysis, 2020, 19 (1) : 145-174. doi: 10.3934/cpaa.2020009 |
[19] |
Sergiy Zhuk. Inverse problems for linear ill-posed differential-algebraic equations with uncertain parameters. Conference Publications, 2011, 2011 (Special) : 1467-1476. doi: 10.3934/proc.2011.2011.1467 |
[20] |
Peter I. Kogut, Olha P. Kupenko. On optimal control problem for an ill-posed strongly nonlinear elliptic equation with $p$-Laplace operator and $L^1$-type of nonlinearity. Discrete and Continuous Dynamical Systems - B, 2019, 24 (3) : 1273-1295. doi: 10.3934/dcdsb.2019016 |
2020 Impact Factor: 1.639
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