Results 21 to 30 of about 900 (183)
A new semilocal convergence theorem for Newton's method [PDF]
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.
JoséM Gutiérrez +2 more
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Center conditions on high order derivatives in the semilocal convergence of Newton’s method
Journal of Complexity, 2015 We modify the classical theory of Kantorovich to analyze the semilocal convergence of Newton's method in Banach spaces under center conditions for high order derivatives. As a consequence, we obtain a modification of the domain of the starting points for Newton's method.
José Antonio Ezquerro +1 more
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Semilocal Convergence of a Multi-Step Parametric Family of Iterative Methods
Symmetry, 2023 In this paper, we deal with a new family of iterative methods for approximating the solution of nonlinear systems for non-differentiable operators. The novelty of this family is that it is a m-step generalization of the Steffensen-type method by updating the divided difference operator in the first two steps but not in the following ones.
Eva G. Villalba +2 more
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Semilocal Convergence for a Fifth-Order Newton's Method Using Recurrence Relations in Banach Spaces [PDF]
Journal of Applied Mathematics, 2011 We study a modified Newton's method with fifth-order convergence for nonlinear equations in Banach spaces. We make an attempt to establish the semilocal convergence of this method by using recurrence relations. The recurrence relations for the method are
Liang Chen, Chuanqing Gu, Yanfang Ma
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Kantorovich-type semilocal convergence analysis for inexact Newton methods
Journal of Computational and Applied Mathematics, 2011 The article deals with the iteration \[ x_{n+1} = x_n - F'(x_n)^{-1}(F(x_n) + r_n), \quad n = 0,1,2,\dots \] for approximately solving a nonlinear operator equation \(F(x) = 0\) with an operator \(F\) acting between two Banach spaces \(X\) and \(Y\). The authors formulate some natural conditions under that the iteration under consideration converges to
Ioannis K. Argyros, Hongmin Ren
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Semilocal convergence conditions for the secant method, using recurrent functions
Journal of Numerical Analysis and Approximation Theory, 2011 Using our new concept of recurrent functions, we present new sufficient convergence conditions for the secant method to a locally unique solution of a nonlinear equation in a Banach space.
Ioannis K. Argyros, Saïd Hilout
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On the semilocal convergence of derivative free methods for solving nonlinear equations
Journal of Numerical Analysis and Approximation Theory, 2012 We introduce a Derivative Free Method (DFM) for solving nonlinear equations in a Banach space setting. We provide a semilocal convergence analysis for DFM using recurrence relations. Numerical examples validating our theoretical results are also provided
Ioannis K. Argyros, Hongmin Ren
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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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