Results 21 to 30 of about 7,885 (185)
Developments of Newton’s Method under Hölder Conditions
European Journal of Mathematical Analysis, 2022 The semi-local convergence criteria for Newton’s method are weakened without new conditions. Moreover, tighter error distances are provided as well as a more precise information on the location of the solution.
Samundra Regmi +3 more
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Generalized Differentiability Conditions for Newton's Method. [PDF]
, 2002 The use of majorizing sequences is the usual way to prove the convergence of Newton's method. An alternative technique to majorizing sequences is provided in this paper, in which three scalar sequences are used, so that the analysis of convergence is ...
Ezquerro, J.A. [0000-0001-8120-167X] +1 more
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Majorizing sequences for Newton's method from initial value problems [PDF]
, 2012 The most restrictive condition used by Kantorovich for proving the semilocal convergence of Newton's method in Banach spaces is relaxed in this paper, providing we can guarantee the semilocal convergence in situations that Kantorovich cannot.
Hernández, null [0000-0001-5478-2958] +2 more
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A generalized multivariable Newton method [PDF]
Fixed Point Theory and Algorithms for Sciences and Engineering, 2021 AbstractIt is well known that the Newton method may not converge when the initial guess does not belong to a specific quadratic convergence region. We propose a family of new variants of the Newton method with the potential advantage of having a larger convergence region as well as more desirable properties near a solution.
Regina S. Burachik +2 more
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Computers & Mathematics with Applications, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Owe Axelsson, Stanislav Sysala
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Accelerated convergence in Newton's method for approximating square roots [PDF]
, 2005 In this paper, we construct a modification of Newton's method to accelerate the convergence of this method to the approximation of the positive square root of a positive real number.
Romero, N. [0000-0002-0653-560X] +3 more
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A modification of the classical Kantorovich conditions for Newton's method [PDF]
, 2001 In the classical Kantorovich theorem on Newton's method it is assumed that the second Fréchet derivative of the involved operator satisfies the condition ||F″(x)||⩽K in an appropiate domain.
Hernández, null [0000-0001-5478-2958] +1 more
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A semilocal convergence result for Newton's method under generalized conditions of Kantorovich [PDF]
, 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
Hernández-Verón, M.A. [0000-0001-5478-2958] +2 more
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WIREs Computational Statistics, 2010 AbstractNewton's method is one of the most powerful techniques for solving systems of nonlinear equations and minimizing functions. It is easy to implement and has a provably fast rate of convergence under fairly mild assumptions. Because of these and other nice properties, Newton's method is at the heart of many solution techniques used to solve real ...
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A new semilocal convergence theorem for Newton's method [PDF]
, 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 ...
JoséM Gutiérrez +2 more
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