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On the semilocal convergence of Newton–Kantorovich method under center-Lipschitz conditions
Applied Mathematics and Computation, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gutiérrez, J. M. +2 more
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On the Newton-Kantorovich method inK-normed spaces
Rendiconti del Circolo Matematico di Palermo, 2000The nonlinear operator equation \( f(x) + g(x) = 0 \) in \(K\)-normed spaces is analysed, where \(f\) is differentiable but \(g\) is not. Here \(K\) is a closed convex regular cone in a real Banach space. Under reasonable assumptions, esp. \(f'\) and \(g\) being Lipschitz in some ball, the authors prove solvability by means of the convergence of a ...
Caponetti, Diana +2 more
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Inverse Problems And The Newton-Kantorovich Method
SPIE Proceedings, 1985The 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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Estimates of Majorizing Sequences in the Newton–Kantorovich Method
Numerical Functional Analysis and Optimization, 2006Let f:B(x 0,R) ⊆ X → Y be an operator, with X and Y Banach spaces, and f′ be Holder continuous with exponent θ. The convergence of the sequence of Newton–Kantorovich approximations is a classical tool to solve the equation f(x) = 0. The convergence of x n is often reduced to the study of the majorizing sequence r n defined by with a, b, k parameters ...
CIANCIARUSO, Filomena +1 more
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On q-Newton–Kantorovich method for solving systems of equations
Applied Mathematics and Computation, 2005It is well known that the classical Newton-Kantorovich method, Halley's method and many others in the class of methods devoted to solving a nonlinear equation \(F(x)=0\), are obtained by considering a corresponding truncated Taylor expansion of \(F\). This happens in the framework of the usual calculus. In the paper under review, by using the so called
Rajković, Predrag M. +2 more
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Newton-Kantorovich Method and Its Global Convergence
Journal of Mathematical Sciences, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On Newton-Kantorovich Method for Profile Reconstruction of Conductor Cylinder
Journal of Electromagnetic Waves and Applications, 1997Summary: 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, C., Gao, D., Wang, W., Jiang, Y.
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On Approximate Solutions of Nonlinear Boundary-Value Problems by the Newton–Kantorovich Method
Journal of Mathematical Sciences, 2021In 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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The Newton-Kantorovich Convergence Theoremf or a Deformed Newton Method
2012 International Conference on Industrial Control and Electronics Engineering, 2012In 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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