Results 11 to 20 of about 3,416 (193)
A new semilocal convergence theorem for Newton's method
Journal of Computational and Applied Mathematics, 1997 A new semilocal convergence theorem for Newton's method is established for solving a nonlinear equation F(x)=0, defined in Banach spaces. It is assumed that the operator F is twice Fréchet differentiable, and F″ satisfies a Lipschitz type condition. Results on uniqueness of solution and error estimates are also given.
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A semilocal convergence result for Newton’s method under generalized conditions of Kantorovich
Journal of Complexity, 2014 From Kantorovich's theory we establish a general semilocal convergence result for Newton's method based fundamentally on a generalization required to the second derivative of the operator involved. As a consequence, we obtain a modification of the domain of starting points for Newton's method and improve the a priori error estimates.
Ezquerro, J.A. +2 more
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A semilocal convergence analysis for the method of tangent parabolas
Journal of Numerical Analysis and Approximation Theory, 2005 We present a semilocal convergence analysis for the method of tangent parabolas (Euler-Chebyshev) using a combination of Lipschitz and center Lipschitz conditions on the Fréchet derivatives involved. This way we produce a majorizing sequence which converges under weaker conditions than before.
Ioannis K. Argyros
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Mathematics, 2021 In this paper, we construct and study a new family of multi-point Ehrlich-type iterative methods for approximating all the zeros of a uni-variate polynomial simultaneously.
Petko D. Proinov, Milena D. Petkova
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A New Family of High-Order Ehrlich-Type Iterative Methods
Mathematics, 2021 One of the famous third-order iterative methods for finding simultaneously all the zeros of a polynomial was introduced by Ehrlich in 1967. In this paper, we construct a new family of high-order iterative methods as a combination of Ehrlich’s iteration ...
Petko D. Proinov, Maria T. Vasileva
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A NOTE ON THE SEMILOCAL CONVERGENCE OF CHEBYSHEV’S METHOD [PDF]
Bulletin of the Australian Mathematical Society, 2012 AbstractIn this paper we develop a Kantorovich-like theory for Chebyshev’s method, a well-known iterative method for solving nonlinear equations in Banach spaces. We improve the results obtained previously by considering Chebyshev’s method as an element of a family of iterative processes.
Diloné, Manuel A. +2 more
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Mathematics, 2022 To deal with the estimation of the locally unique solutions of nonlinear systems in Banach spaces, the local as well as semilocal convergence analysis is established for two higher order iterative methods. The given methods do not involve the computation
Janak Raj Sharma +2 more
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Improving Convergence Analysis of the Newton–Kurchatov Method under Weak Conditions
Computation, 2020 The technique of using the restricted convergence region is applied to study a semilocal convergence of the Newton−Kurchatov method. The analysis is provided under weak conditions for the derivatives and the first order divided differences ...
Ioannis K. Argyros +2 more
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Fractal and Fractional, 2023 Local convergence of order three has been established for the Newton–Simpson method (NS), provided that derivatives up to order four exist. However, these derivatives may not exist and the NS can converge.
Santhosh George +4 more
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Electronic structure and phase stability of oxide semiconductors: Performance of dielectric-dependent hybrid functional DFT, benchmarked against $GW$ band structure calculations and experiments [PDF]
, 2015 We investigate band gaps, equilibrium structures, and phase stabilities of several bulk polymorphs of wide-gap oxide semiconductors ZnO, TiO2,ZrO2, and WO3. We are particularly concerned with assessing the performance of hybrid functionals built with the
Bottani, Carlo Enrico +5 more
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