Topological cones, operator equations, and the Newton-Kantorovich method
Mathematical Notes of the Academy of Sciences of the USSR, 1983Translation from Mat. Zametki 33, No.1, 65-70 (Russian) (1983; Zbl 0508.47013).
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Gradient and Newton-Kantorovich Methods for Microwave Tomography
1997The development of reconstruction algorithms for Active Microwave Imaging, with applications in the medical domain or for non-destructive testing [1], and more generally for electromagnetic and acoustic imaging [2], has gained much interest during the last decade.
Christian Pichot +6 more
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Convergence of the Newton--Kantorovich Method for Calculating Invariant Subspaces
Mathematical Notes, 2004We propose a version of the Newton--Kantorovich method which, given a nondegenerate square n X n matrix and a number ...
Yu. M. Nechepurenko, M. Sadkane
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An asymptotic relation for the iteratively regularized newton-kantorovich method
USSR Computational Mathematics and Mathematical Physics, 1983Translation from Zh. Vychisl. Mat. Mat. Fiz. 23, No.1, 216-218 (Russian) (1983; Zbl 0536.65043).
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Improved estimates on majorizing sequences for the Newton–Kantorovich method
Journal of Applied Mathematics and Computing, 2009The 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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Convergence of the Newton-Kantorovich Method under Vertgeim Conditions: a New Improvement
Zeitschrift für Analysis und ihre Anwendungen, 1998Let f: B(x_0, R) \subset X \to Y be an operator from a closed ball of a Banach space X to a Banach space Y
De Pascale, E., Zabreiko, P. P.
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A strengthened Newton-Kantorovich method with approximation of the inverse operator
USSR Computational Mathematics and Mathematical Physics, 1972Abstract 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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On the equivalence of the Newton-Kantorovich and distorted Born methods
Inverse Problems, 2000Summary: 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, 1996We 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 +3 more
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Newton–Kantorovich type convergence theorem for a family of new deformed Chebyshev method
Applied Mathematics and Computation, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wu, Qingbiao, Zhao, Yueqing
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