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Frozen Landweber Iteration for Nonlinear Ill-Posed Problems
Acta Mathematicae Applicatae Sinica, English Series, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xu, J., Han, B., Li, L.
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An Efficient Discretization Scheme for Solving Nonlinear Ill-Posed Problems
Computational Methods in Applied Mathematics, 2023Abstract Information based complexity analysis in computing the solution of various practical problems is of great importance in recent years. The amount of discrete information required to compute the solution plays an important role in the computational complexity of the problem. Although this approach has been applied successfully for
M. P. Rajan, Jaise Jose
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Tikhonov regularization for nonlinear ill-posed problems
Nonlinear Analysis: Theory, Methods & Applications, 1997Let \(F: D(F) \subset X \to Y\) be a weakly closed, continuous, Fréchet differentiable mapping with convex domain \(D(F)\) between the real Hilbert spaces \(X\) and \(Y\). The paper develops from results of \textit{O. Scherzer, H. W. Engl} and \textit{K. Kunisch} [SIAM J. Numer. Anal. 30, No.
Hou, Zongyi, Jin, Qinian
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Modified Minimal Error Method for Nonlinear Ill-Posed Problems
Computational Methods in Applied Mathematics, 2017Abstract An error estimate for the minimal error method for nonlinear ill-posed problems under general a Hölder-type source condition is not known. We consider a modified minimal error method for nonlinear ill-posed problems. Using a Hölder-type source condition, we obtain an optimal order error estimate.
Sabari, M., George, Santhosh
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Multilevel augmentation methods for nonlinear ill-posed problems
International Journal of Computer Mathematics, 2011We propose multilevel augmentation methods for solving nonlinear ill-posed problems, involving monotone operators in the Hilbert space by using the Lavrentiev regularization method. This leads to a fast solutions of the discrete regularization methods for the nonlinear ill-posed equations.
Shengpei Ding, Hongqi Yang
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Nonlinear implicit iterative method for solving nonlinear ill-posed problems
Applied Mathematics and Mechanics, 2009The authors study the iterated Tikhonov regularization method for solving nonlinear ill-posed problems and prove its convergence under some conditions. Reviewer's notes: The directly related papers by \textit{O. Scherzer} [Numer. Math. 66, No.~2, 259--279 (1993; Zbl 0791.65040)] and by \textit{Q.-N. Jin} and \textit{Z.-Y. Hou} [Inverse Probl. 13, No.~3,
Liu, Jianjun +2 more
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Iterative Regularization Methods for Nonlinear Ill-Posed Problems
2008The series is devoted to the publication of high-level monographs, surveys and proceedings which cover the whole spectrum of computational and applied mathematics. The books of this series are addressed to both specialists and advanced students. Interested authors may submit book proposals to the Managing Editor or to any member of the Editorial Board.
Barbara Kaltenbacher +2 more
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On the Landweber iteration for nonlinear ill-posed problems
Journal of Inverse and Ill-Posed Problems, 1996Consider the nonlinear operator equation \[ F(x)=y. \tag{1} \] Here, \(F:D(F)\subseteq X\to Y\) is a nonlinear map between Hilbert spaces \(X\) and \(Y\). The problem of solving (1) is called ill posed if the solution \(x_*\) does not depend continuously on the right-hand side \(y\). It is assumed that (1) is ill posed.
Binder, A., Hanke, M., Scherzer, O.
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Regularizing Newton--Kaczmarz Methods for Nonlinear Ill-Posed Problems
SIAM Journal on Numerical Analysis, 2006We introduce a class of stabilizing Newton--Kaczmarz methods for nonlinear ill-posed problems and analyze their convergence and regularization behavior. As usual for iterative methods for solving nonlinear ill-posed problems, conditions on the nonlinearity (or the derivatives) have to be imposed in order to obtain convergence.
Martin Burger, Barbara Kaltenbacher
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A regularization method for nonlinear ill-posed problems
Computer Physics Communications, 1993Abstract Often, physically interesting functions are not directly accessible by an experiment, and must be calculated from data of an experimental accessible quantity. If this calculation requires the inversion of a Fredholm integral equation of the first kind, the determination of the physically interesting function is an ill-posed problem.
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