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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
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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.
Qingbiao Wu
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A Newton–Kantorovich convergence theorem for the inverse-free Jarratt method in Banach space
Applied Mathematics and Computation, 2006Under weak conditions, we establish a Newton-Kantorovich type convergence theorem of the inverse-free Jarratt method in Banach space which is used to solve a nonlinear operator equation. Finally, some examples are provided to show the applicability of our theorem.
Qingbiao Wu
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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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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
Predrag M. Rajkovic +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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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, Chunyang +3 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 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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