Results 121 to 130 of about 182 (158)

Inverse Problems And The Newton-Kantorovich Method

SPIE Proceedings, 1985
The use of nonlinear operator equation techniques, and the Newton-Kantorovich method in particular, to solve inverse problems is outlined. The application of the method to two problems - inverse refractive index scattering and an inverse problem of steady-state diffusion - is then considered.
T. J. Connolly, D. J. Wall, R. H. Bates
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On Newton-Kantorovich Method for Profile Reconstruction of Conductor Cylinder

Journal of Electromagnetic Waves and Applications, 1997
Summary: Fréchet differential corresponding to the inverse scattering of conductor cylinder is studied by adjoint operator theory. Numerical implementation of Newton-Kantorovich algorithm under successive plane wave illumination of different directions and frequencies is presented. Determination of initial values for iteration is introduced.
Yu, Chunyang, Gao, Deyuan, Wang, Wenbing, Jiang, Yansheng   +3 more
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Newton-Kantorovich Method and Its Global Convergence

Journal of Mathematical Sciences, 2006
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On Approximate Solutions of Nonlinear Boundary-Value Problems by the Newton–Kantorovich Method

Journal of Mathematical Sciences, 2021
In this paper, the authors establish necessary and sufficient conditions for the solvability of a nonlinear boundary-value problem in the critical case. They develop a scheme for the construction of solutions of this problem by using the Newton-Kantorovich method.
Boichuk, A. A., Chuiko, S. M.
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On the equivalence of the Newton-Kantorovich and distorted Born methods

Inverse Problems, 2000
Summary: We show that the Newton-Kantorovich and distorted Born methods for the computational solution of the nonlinear inverse scattering problem are equivalent. This was already shown for the discrete matrix case. Here, we present an analysis based on the analytic representations of the integral operators.
Remis, R. F., van den Berg, P. M.
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On the Application of the Newton–Kantorovich Method to Nonlinear Partial Integral Equations

Zeitschrift für Analysis und ihre Anwendungen, 1996
We discuss the applicability of the Newton–Kantorovich method to a nonlinear equation which contains partial integrals with Uryson type kernels. A basic ingredient of this method consists in verifying a local Lipschitz condition for the Fréchet derivatives of the nonlinear partial integral operators generated by such kernels.
Appell, Jürgen, De Pascale, Espedito, Kalitvin, A. S., Zabrejko, P. P.   +3 more
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An asymptotic relation for the iteratively regularized newton-kantorovich method

USSR Computational Mathematics and Mathematical Physics, 1983
Translation from Zh. Vychisl. Mat. Mat. Fiz. 23, No.1, 216-218 (Russian) (1983; Zbl 0536.65043).
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A strengthened Newton-Kantorovich method with approximation of the inverse operator

USSR Computational Mathematics and Mathematical Physics, 1972
Abstract THE convergence of the method of solving the equation P(x) = 0, indicated in the title, with replacement of the operator [P′(xn)]−1 by some approximation of it, is investigated. Many iterative methods of solving the equation (1) P(x) = 0 are constructed in such a way that to find x it is necessary to calculate [P′(xn)]−1 on some element yn.
Verzhbitskij, V. M., Tsalyuk, Z. B.
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Improved estimates on majorizing sequences for the Newton–Kantorovich method

Journal of Applied Mathematics and Computing, 2009
The author approximates the locally unique solution \(x^*\) of the equation \(F(x)=0\), where \(F\) is a Fréchet differentiable operator mapping a convex subset \(D\) of a Banach space \(X\) in a Banach space \(Y\). The most popular method generating a sequence \(\{x_{n}\}\) is the Newton-Kantorovitch method: \[ x_{n+1}=x_{n}-F'(x_{n})^{-1}F'(x_{n ...
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The Newton-Kantorovich Convergence Theoremf or a Deformed Newton Method

2012 International Conference on Industrial Control and Electronics Engineering, 2012
In this study, we establish the Newton-Kantorovich convergence theorem with three orders for a deformed Newton methods in Banach space by using two orders majorizing function, which is used to solve the nonlinear operator equation. We also present the error estimate. Finally, the examples are provided to show the application of our theorem.
Rongfei Lin, Yueqing Zhao
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