Results 121 to 130 of about 2,383 (165)

A homotopy regularization method for nonlinear ill-posed problems

2011 International Conference on Multimedia Technology, 2011
We report on a new method for nonlinear ill-posed operator equation in Hilbert spaces. Based on the principle of the homotopy method, a new functional is introduced to replace the Tikhonov functional. The minimizer of this replacement functional will constitute a continuous curve connecting the initial value with the approximate solution of the ...
Hongsun Fu, Bo Han
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Optimization Tools for Solving Nonlinear Ill-posed Problems

2001
Using the L- and a-curve, we consider how a nonlinear ill-posed Tikhonov regularized problem can be solved by a Gauss-Newton method. The solution to the problem is chosen from the point on the logarithmic L-curve that has maximal curvature, i.e. at the corner.
Thomas Viklands, Marten Gulliksson
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A direct method for nonlinear ill-posed problems

Inverse Problems, 2017
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A GCV based method for nonlinear ill-posed problems

Computational Geosciences, 2000
The authors deal with the solution of the nonlinear ill-posed equation \(F(m)=b\), where \(F:\mathbb{R}^M \to\mathbb{R}^N\) is a differentiable operator with \(M >N\), and right-hand side \(b\) is noisy. Let \(\phi(\beta, m)=\|F(m)-b\|^2+ \beta \|W(m-m_{\text{ref}}) \|^2\) be the Tikhonov functional of the problem.
Haber, Eldad, Oldenburg, Douglas
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TIGRA an iterative algorithm for regularizing nonlinear ill-posed problems

Inverse Problems, 2003
A sophisticated numerical analysis of a combination of Tikhonov regularization and the gradient method for solving nonlinear ill-posed problems is presented. The TIGRA (Tikhonov-gradient method) algorithm proposed uses steepest descent iterations in an inner loop for approximating the Tikhonov regularized solutions with a fixed regularization parameter
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On the asymptotical regularization of nonlinear ill-posed problems

Inverse Problems, 1994
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A dynamical system method for solving nonlinear ill-posed problems

Applied Mathematics and Computation, 2008
Nonlinear ill-posed operator equations of the type \(F(t,u(t))=z(t)\), where \(F\) is a Fréchet differentiable operator acting between two Hilbert spaces may be solved approximately by the dynamical system method that regularizes the problem. Employing Lyapunov's theory, the authors study stability of the approximate solutions as well as convergence ...
Li, Li, Han, Bo
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A Simplified Landweber Iteration for Solving Nonlinear Ill-Posed Problems

International Journal of Applied and Computational Mathematics, 2017
Landweber iterative method is one of the well-known techniques used for solving nonlinear ill-posed problems. The convergence analysis and error estimates are usually derived with many assumptions which are very difficult to verify from a practical point of view.
Jaise Jose, M. P. Rajan
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Regularization method with two parameters for nonlinear ill-posed problems

Science in China Series A: Mathematics, 2008
The paper is concerned with solution methods for ill-posed operator inclusions \(y_0 \in F(x)\) \((x \in D(F))\) in a Banach space \(X\). The authors establish the convergence of multivalued Tikhonov's regularization method \[ \inf_{x \in D(F)} \inf_{y \in F(x)} \{ \| y-y_0\|^2+ \alpha \| Lx-Lx^* \|^2+ \beta \| x\|^2 \}, \] where \(L\) is a closed ...
Liu, ZhenHai, Li, Jing, Li, ZhaoWen
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Iterative Runge–Kutta-type methods for nonlinear ill-posed problems

Inverse Problems, 2008
We present a regularization method for solving nonlinear ill-posed problems by applying the family of Runge–Kutta methods to an initial value problem, in particular, to the asymptotical regularization method. We prove that the developed iterative regularization method converges to a solution under certain conditions and with a general stopping rule ...
C Böckmann, P Pornsawad
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