Results 1 to 10 of about 2,363 (145)
A Modified Asymptotical Regularization of Nonlinear Ill-Posed Problems [PDF]
Mathematics, 2019 In this paper, we investigate the continuous version of modified iterative Runge–Kutta-type methods for nonlinear inverse ill-posed problems proposed in a previous work.
Pornsarp Pornsawad +2 more
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Newton-Type Iteration for Tikhonov Regularization of Nonlinear Ill-Posed Problems [PDF]
Journal of Mathematics, 2013 Recently in the work of George, 2010, we considered a modified Gauss-Newton method for approximate solution of a nonlinear ill-posed operator equationF(x)=y, whereF:D(F)⊆X→Yis a nonlinear operator between the Hilbert spacesXandY. The analysis in George, 2010 was carried out using a majorizing sequence. In this paper, we consider also the modified Gauss-
Santhosh George
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Impact of ISTA and FISTA iterative optimization algorithms on electrical impedance tomography image reconstruction. [PDF]
J Electr BioimpedanceElectrical Impedance Tomography (EIT) is a non-invasive method for imaging conductivity distributions within a target area. The inverse problem associated with EIT is nonlinear and ill-posed, leading to low spatial resolution reconstructions.
Nguyen Diep QT +5 more
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Mathematics, 2021 We prove the logarithmic convergence rate of the families of usual and modified iterative Runge-Kutta methods for nonlinear ill-posed problems between Hilbert spaces under the logarithmic source condition, and numerically verify the obtained results. The
Pornsarp Pornsawad +2 more
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Iterated Lavrentiev regularization for nonlinear ill-posed problems [PDF]
ANZIAM Journal, 2009 AbstractWe consider an iterated form of Lavrentiev regularization, using a null sequence (αk) of positive real numbers to obtain a stable approximate solution for ill-posed nonlinear equations of the form F(x)=y, where F:D(F)⊆X→X is a nonlinear operator and X is a Hilbert space.
Mahale, P., Nair, M. T.
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Recent Advances in the Geodesy Data Processing [PDF]
Journal of Geodesy and Geoinformation Science, 2023 Geodetic functional models, stochastic models, and model parameter estimation theory are fundamental for geodetic data processing. In the past five years, through the unremitting efforts of Chinese scholars in the field of geodetic data processing ...
Jianjun ZHU, Leyang WANG, Jun HU, Bofeng LI, Haiqiang FU, Yibin YAO
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Some approximate Gauss–Newton-type methods for nonlinear ill-posed problems; pp. 227–237 [PDF]
Proceedings of the Estonian Academy of Sciences, 2013 This paper treats numerical methods for solving the nonlinear ill-posed equation F(x) = 0, where the operator F is a Fréchet differentiable operator from one Hilbert space into another Hilbert space.
Inga Kangro, Raul Kangro, Otu Vaarmann
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Identification of linear response functions from arbitrary perturbation experiments in the presence of noise – Part 1: Method development and toy model demonstration [PDF]
Nonlinear Processes in Geophysics, 2021 Existent methods to identify linear response functions from data require tailored perturbation experiments, e.g., impulse or step experiments, and if the system is noisy, these experiments need to be repeated several times to obtain good statistics.
G. L. Torres Mendonça +4 more
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Parameter Identification for Nonlinear Ill-Posed Problems [PDF]
Mathematical and Computational Applications, 2010 Since the classical iterative methods for solving nonlinear ill-posed problems are locally convergent, this paper constructs a robust and widely convergent method for identifying parameter based on homotopy algorithm, and investigates this method’s convergence in the light of Lyapunov theory.
Li, Li, Han, Bo
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Mathematics, 2023 In this paper, we consider a generalized inexact Newton-Landweber iteration to solve nonlinear ill-posed inverse problems in Banach spaces, where the forward operator might not be Gâteaux differentiable.
Ruixue Gu, Hongsun Fu, Zhuoyue Wang
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