Results 261 to 270 of about 12,109 (301)

JULIA SETS OF GENERALIZED NEWTON'S METHOD

Fractals, 2007
The Julia sets theory of generalized Newton's method is analyzed and the Julia sets of generalized Newton's method are constructed using the iteration method. From the research we find that: (1) the basins of attraction of the Julia sets of generalized Newton's method depend on the roots of the equation and their orders and also the existence of the ...
Wang, Xingyuan, Wang, Tingting
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Newton's Method for a Generalized Inverse Eigenvalue Problem

Numerical Linear Algebra with Applications, 1997
A family of matrices \(A(c)\) and \(B(c)\) dependent on a vector \(c=(c_1,\dots,c_n)\in \Omega \subset \mathbb R^n\) is introduced, \(A(c)=A_0+\sum_{k=1}^n c_kA_k\), \(B(c)=B_0+\sum_{k=1}^n c_kB_k\), \(B(c)>0\), where \(A_k,B_k\), \(k=0,\dots n\), are given real symmetric matrices.
Hua Dai, Peter Lancaster
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Generalized Nash equilibrium problems and Newton methods

Mathematical Programming, 2007
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Francisco Facchinei, Andreas Fischer 0004, Veronica Piccialli   +2 more
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Remarks on the generalized Newton method

Mathematical Programming, 1993
Let \(H\) be a Hilbert space, \(f: H\to H\) a continuously Gâteaux differentiable function and \(g: H\to H\) a multivalued mapping. For the numerical solution of the problem \(f(u)+ g(u)\ni 0\), the generalized Newton method \(u_{n+1}= (f'(u_ n)+ g)^{-1}(f'(u_ n)[u_ n]- f(u_ n))\) is considered. For the case when \(g\) is the subdifferential mapping of
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Convergence of an inexact generalized Newton method with a scaled residual control

Computers and Mathematics With Applications, 2011
The inexact generalized Newton method is an iterative method for solving systems of nonsmooth equations. In this paper, the iterative process with a relative residual control is presented and the conditions for local convergence to a solution are ...
Marek J Śmietański
exaly   +2 more sources

Convergence of inexact Newton methods for generalized equations

Mathematical Programming, 2013
For general inclusions of the form ``zero is contained in \(f(x) + F(x)\)'', where \(f\) is a smooth function and \(F\) a set-valued mapping both acting between Banach spaces, the authors study local properties of inexact Newton methods. As main results they get conditions such that the considered iteration sequences have ``no halt'', that means they ...
Asen L. Dontchev, R. Tyrrell Rockafellar
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Generalized Newton-iterative method for semismooth equations

Numerical Algorithms, 2011
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Zhe Sun, Jinping Zeng, Hongru Xu
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A generalized Newton–Raphson method using curvature

Communications in Numerical Methods in Engineering, 1995
AbstractA numerical method for finding the roots of any function is developed. This method considers a circle using the concept of curvature instead of the tangential line in the Newton‐Raphson method. The compared results between the proposed method and the Newton‐Raphson method are listed.
Lee, IW Lee, In Won, JUNG, GH JUNG, GH
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Spurious singularities in the generalized Newton variational method

Physical Review A, 1991
The generalized Newton variational method is applied to the static-exchange approximation of the electron--hydrogen-atom scattering. Slater-type basis functions are employed to expand the amplitude density. Spurious singularities are encountered in both scattering processes.
, Apagyi, , Lévay, , Ladányi
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A Smoothing Newton Method for General Nonlinear Complementarity Problems

Computational Optimization and Applications, 2000
The paper deals with the nonlinear complementarity problem: to find \(x \in \mathbb{R}^n_+\) such that \(F(x) \geq 0\), \(x \geq 0\), \(x^TF(x)=0\), where \(F: \mathbb{R}^n\to \mathbb{R}^n\) is a continuously differentiable function. The authors consider the system: \(H= ( e^{\mu}-1 \Phi_{\mu} (x))^T\), where \(\Phi_{\mu}\) is defined by Kanzow's ...
Houduo Qi, Li-Zhi Liao
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