Local Convergence and Radius of Convergence for Modified Newton Method
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In this paper, the authors investigated the local convergence of modified Newton method, i.e., the classical Newton method in which the derivative is periodically re-evaluated, and they gave an algorithm to estimate the local radius of convergence for considered method.Abstract:
Abstract We investigate the local convergence of modified Newton method, i.e., the classical Newton method in which the derivative is periodically re-evaluated. Based on the convergence properties of Picard iteration for demicontractive mappings, we give an algorithm to estimate the local radius of convergence for considered method. Numerical experiments show that the proposed algorithm gives estimated radii which are very close to or even equal with the best ones.read more
Citations
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Dynamics of Newton-like root finding methods
TL;DR: In this article , the symmetries of the operators obtained after applying Newton-like root finding algorithms to a family of degree d polynomials p ( z ) = z d − c were studied.
References
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Book
Iterative Solution of Nonlinear Equations in Several Variables
J.M. Ortega,Werner C. Rheinboldt +1 more
TL;DR: In this article, the authors present a list of basic reference books for convergence of Minimization Methods in linear algebra and linear algebra with a focus on convergence under partial ordering.
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Approximating fixed points of nonexpansive mappings
H. F. Senter,W. G. Dotson +1 more
TL;DR: In this article, it was shown that if T satisfies one additional condition, which is weaker than the requirement that T be demicompact, then an iterative process of the type introduced by W. R. Mann [8] converges to a fixed point of T.
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