Results 151 to 160 of about 11,230,834 (184)

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 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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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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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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Topological cones, operator equations, and the Newton-Kantorovich method

Mathematical Notes of the Academy of Sciences of the USSR, 1983
Translation from Mat. Zametki 33, No.1, 65-70 (Russian) (1983; Zbl 0508.47013).
openaire   +3 more sources

Convergence of the Newton--Kantorovich Method for Calculating Invariant Subspaces

Mathematical Notes, 2004
We 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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Gradient and Newton-Kantorovich Methods for Microwave Tomography

1997
The 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, Pierre Lobel, Laure Blanc-Féraud, Michel Barlaud, Kamal Belkebir, Jean-Manuel Elissalt, Jean-Michel Geffrin   +6 more
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Convergence of the Newton-Kantorovich Method under Vertgeim Conditions: a New Improvement

Zeitschrift für Analysis und ihre Anwendungen, 1998
Let 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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On the approximate solution of an autonomous boundary-value problem by the Newton–Kantorovich method

Journal of Mathematical Sciences, 2013
The authors propose an iterative approximation scheme for the second-order boundary value problem \[ z''=Az+Bz'+f+\varepsilon Z\left(z,z',\varepsilon\right)\text{, }\,\ell z(\cdot,\varepsilon)=\alpha+\varepsilon J\left(z(\cdot,\varepsilon),z'(\cdot,\varepsilon),\varepsilon\right), \] where standard regularity hypotheses are imposed on the function \(Z\)
Chuiko, S. M., Boichuk, I. A., Pirus, O. E.   +2 more
openaire   +1 more source