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Newton's method and regularly smooth operators
Journal of Numerical Analysis and Approximation Theory, 2011 A semilocal convergence analysis for Newton's method in a Banach space setting is provided in this study. Using a combination of regularly smooth and center regularly smooth conditions on the operator involved, we obtain more precise majorizing sequences
Ioannis K. Argyros
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On Newton's method for subanalytic equations
Journal of Numerical Analysis and Approximation Theory, 2017 We present local and semilocal convergence results for Newton’s method in order to approximate solutions of subanalytic equations. The local convergence results are given under weaker conditions than in earlier studies such as [9], [10], [14], [15], [24]
Ioannis K. Argyros, Santhosh George
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Fractional Newton-Raphson Method
Applied Mathematics and Sciences An International Journal (MathSJ), 2021 The Newton-Raphson (N-R) method is useful to find the roots of a polynomial of degree n, with n ∈ N. However, this method is limited since it diverges for the case in which polynomials only have complex roots if a real initial condition is taken. In the present work, we explain an iterative method that is created using the fractional calculus, which we
Torres Hernandez, Anthony +1 more
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Transforming common-sense beliefs into Newtonian thinking through Just-In-Time Teaching
Physical Review Special Topics. Physics Education Research, 2010 To determine whether teaching an introductory physics course with a traditional lecture style or with Just-in-Time teaching (a student-centered, interactive-engagement style) will help students to better understand Newtonian concepts, such as Newton’s ...
Sarah P. Formica +2 more
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Newton-Product Integration for a Stefan Problem with Kinetics [PDF]
Journal of Sciences, Islamic Republic of Iran, 2011 Stefan problem with kinetics is reduced to a system of nonlinear Volterra integral equations of second kind and Newton's method is applied to linearize it. Product integration solution of the linear form is found and sufficient conditions for convergence
K. Ivaz
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Journal of Numerical Analysis and Approximation Theory, 2007 In this study we are concerned with the problem of approximating a locally unique solution of an equation in a Banach space setting using Newton's and modified Newton's methods. We provide weaker convergence conditions for both methods than before [6]-[8]
Ioannis Argyros
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Generalized Newton's Method based on Graphical Derivatives [PDF]
, 2010 This paper concerns developing a numerical method of the Newton type to solve systems of nonlinear equations described by nonsmooth continuous functions. We propose and justify a new generalized Newton algorithm based on graphical derivatives, which have
Hoheisel, T. +3 more
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Newton's method in the context of gradients
Electronic Journal of Differential Equations, 2007 This paper gives a common theoretical treatment for gradient and Newton type methods for general classes of problems. First, for Euler-Lagrange equations Newton's method is characterized as an (asymptotically) optimal variable steepest descent method ...
John W. Neuberger, Janos Karatson
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Improving Newton's method performance by parametrization: the case of Richards equation [PDF]
, 2016 The nonlinear systems obtained by discretizing degenerate parabolic equations may be hard to solve, especially with Newton's method. In this paper, we apply to Richards equation a strategy that consists in defining a new primary unknown for the ...
Brenner, Konstantin, Cancès, Clément
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Numerical Analysis of Time-Accurate Solution of Nonlinear Flow Models by Implicit Finite Differences
Nonlinear Analysis, 2003 Implicit finite differences are often applied to solve flow models. A standard technique to solve these equations is Newton's method. lf time step is too large although the difference equation could be computationally stable, Newton's method may fail ...
S. K. Dey
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