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Augmented Tikhonov Regularization Method for Dynamic Load Identification [PDF]
Applied Sciences, 2020 We introduce the augmented Tikhonov regularization method motivated by Bayesian principle to improve the load identification accuracy in seriously ill-posed problems.
Jinhui Jiang +4 more
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Projected Newton Method for noise constrained Tikhonov regularization [PDF]
Inverse Problems, 2020 Tikhonov regularization is a popular approach to obtain a meaningful solution for ill-conditioned linear least squares problems. A relatively simple way of choosing a good regularization parameter is given by Morozov's discrepancy principle.
Cornelis, Jeffrey +2 more
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Extrapolation of Tikhonov regularization method
Mathematical Modelling and Analysis, 2010 We consider regularization of linear ill‐posed problem Au = f with noisy data fδ, ¦fδ - f¦≤ δ . The approximate solution is computed as the extrapolated Tikhonov approximation, which is a linear combination of n ≥ 2 Tikhonov approximations with different
Uno Hämarik, Reimo Palm, Toomas Raus
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A GCV based Arnoldi-Tikhonov regularization method [PDF]
BIT Numerical Mathematics, 2013 For the solution of linear discrete ill-posed problems, in this paper we consider the Arnoldi-Tikhonov method coupled with the Generalized Cross Validation for the computation of the regularization parameter at each iteration.
Novati, Paolo, Russo, Maria Rosaria
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The Tikhonov Regularization Method for Set-Valued Variational Inequalities [PDF]
Abstract and Applied Analysis, 2012 This paper aims to establish the Tikhonov regularization theory for set-valued variational inequalities. For this purpose, we firstly prove a very general existence result for set-valued variational inequalities, provided that the mapping involved has ...
Yiran He
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A hybrid splitting method for smoothing Tikhonov regularization problem [PDF]
Journal of Inequalities and Applications, 2016 In this paper, a hybrid splitting method is proposed for solving a smoothing Tikhonov regularization problem. At each iteration, the proposed method solves three subproblems.
Yu-Hua Zeng, Zheng Peng, Yu-Fei Yang
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The Application of Piecewise Regularization Reconstruction to the Calibration of Strain Beams [PDF]
SensorsStandard beams are mainly used for the calibration of strain sensors using their load reconstruction models. However, as an ill-posed inverse problem, the solution to these models often fails to converge, especially when dealing with dynamic loads of ...
Jingjing Liu +7 more
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A Posteriori Fractional Tikhonov Regularization Method for the Problem of Analytic Continuation
Mathematics, 2021 In this paper, the numerical analytic continuation problem is addressed and a fractional Tikhonov regularization method is proposed. The fractional Tikhonov regularization not only overcomes the difficulty of analyzing the ill-posedness of the ...
Xuemin Xue, Xiangtuan Xiong
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Tikhonov regularized iterative methods for nonlinear problems
Optimization, 2023 We consider the monotone inclusion problems in real Hilbert spaces. Proximal splitting algorithms are very popular technique to solve it and generally achieve weak convergence under mild assumptions. Researchers assume the strong conditions like strong convexity or strong monotonicity on the considered operators to prove strong convergence of the ...
Avinash Dixit +3 more
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An Improved Tikhonov-Regularized Variable Projection Algorithm for Separable Nonlinear Least Squares
Axioms, 2021 In this work, we investigate the ill-conditioned problem of a separable, nonlinear least squares model by using the variable projection method. Based on the truncated singular value decomposition method and the Tikhonov regularization method, we propose ...
Hua Guo, Guolin Liu, Luyao Wang
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