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Semilocal convergence for the Super-Halley’s method
Numerical Analysis and Applications, 2014Summary: The semilocal convergence of the super-Halley's method for solving nonlinear equations in Banach spaces is established under the assumption that the second Fréchet derivative satisfies the \(\omega\)-continuity condition. This condition is milder than the well-known Lipschitz and Hölder continuity conditions. The importance of our work lies in
Prashanth, Maroju +2 more
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On semilocal convergence of two step Kurchatov method
International Journal of Computer Mathematics, 2018In this article we present a new semilocal convergence analysis for the two step Kurchatov method by using recurrence relations under Lipschitz type conditions on first-order divided difference ope...
Himanshu Kumar, Pradip Kumar Parida 0001
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New semilocal and local convergence analysis for the Secant method
Applied Mathematics and Computation, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ángel Alberto Magreñán +1 more
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Semilocal convergence of a continuation method in Banach spaces
Numerical Analysis and Applications, 2017Summary: This paper is concerned with the semilocal convergence of a continuation method between two third-order iterative methods, namely, the Halley's and the convex acceleration of Newton's method, also known as the Super-Halley's method. This convergence analysis is discussed using the recurrence relations approach.
Prashanth, Maroju, Motsa, Sandile
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ON THE SEMILOCAL CONVERGENCE OF NEWTON'S METHOD FOR SECTIONS ON RIEMANNIAN MANIFOLDS
Asian-European Journal of Mathematics, 2014We present a semilocal convergence analysis of Newton's method for sections on Riemannian manifolds. Using the notion of a 2-piece L-average Lipschitz condition introduced in [C. Li and J. H. Wang, Newton's method for sections on Riemannian manifolds: Generalized covariant α-theory, J.
Argyros, Ioannis K., George, Santhosh
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SEMILOCAL CONVERGENCE OF A STIRLING-LIKE METHOD IN BANACH SPACES
International Journal of Computational Methods, 2010The aim of this paper is to establish the semilocal convergence of a third order Stirling–like method employed for solving nonlinear equations in Banach spaces by using the first Fréchet derivative, which satisfies the Lipschitz continuity condition.
Parhi, S. K., Gupta, D. K.
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Semilocal convergence of a sixth-order method in Banach spaces
Numerical Algorithms, 2012The paper deals with the approximate solution of a nonlinear equation \(F(x)= 0\), where \(F\) is a mapping of a convex set \(\Omega\) of a Banach space \(X\) in a Banach space \(Y\). It is assumed that \(F\) is Fréchet-differentiable of order 3. To solve the equation numerically we know Newton's method, Chebyshev's method, Halley's method, Newton ...
Lin Zheng 0006, Chuanqing Gu
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Semilocal convergence and R-order for modified Chebyshev-Halley methods
Numerical Algorithms, 2012A nonlinear equation \(F(x)=0\) in Banach spaces is to solve on a nonempty open convex subset of space \(X\), where \(F\) has values in a Banach space \(Y\). Newton's method converges quadratically. Third-order methods use the second Fréchet derivative of \(F\).
Xiuhua Wang 0002, Jisheng Kou
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The semilocal convergence of a generalization of Brent's and Brown's methods
Numerical Algorithms, 1994zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Local and Semilocal Convergence of Wang-Zheng’s Method for Simultaneous Finding Polynomial Zeros
Symmetry, 2019 In 1984, Wang and Zheng (J. Comput. Math. 1984, 1, 70–76) introduced a new fourth order iterative method for the simultaneous computation of all zeros of a polynomial.
Slav Cholakov
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