Results 221 to 230 of about 98,087 (266)

Expanding the applicability of Newton’s method and of a robust modified Newton’s method

Applicationes Mathematicae, 2021
Summary: Newton's method cannot be used to approximate a solution of a nonlinear equation when the derivative of the function is singular or almost singular. To overcome this problem a modified Newton's method may be used. The Newton-Kantorovich theorem is used to show its convergence. The convergence domain of this method is small in general.
Argyros, Ioannis K., George, Santhosh
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On the Gauss–Newton method

Journal of Applied Mathematics and Computing, 2010
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Argyros, Ioannis K., Hilout, Saïd
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Inexact Newton Methods

SIAM Journal on Numerical Analysis, 1982
A classical algorithm for solving the system of nonlinear equations $F(x) = 0$ is Newton’s method \[ x_{k + 1} = x_k + s_k ,\quad {\text{where }}F'(x_k )s_k = - F(x_k ),\quad x_0 {\text{ given}}.\]...
Dembo, Ron S., Eisenstat, Stanley C., Steihaug, Trond   +2 more
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A parameterized Newton method and a quasi-Newton method for nonsmooth equations

Computational Optimization and Applications, 1994
Two methods are discussed for solving nonsmooth equations. The first method, a parametrized Newton method, uses a damping parameter for the Newton step and a regularization parameter for the chosen member of the generalized Jacobian, and, therefore, is well-defined even when the generalized Jacobian is singular.
Xiaojun Chen 0001, Liqun Qi 0001
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Perturbation Lemma for the Newton Method with Application to the SQP Newton Method

Journal of Optimization Theory and Applications, 1998
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Cores, D., Tapia, R. A.
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GENERALIZATIONS OF NEWTON'S METHOD

Fractals, 2001
We give a survey of the complex dynamics of various generalizations of Newton's method for finding a complex root of a polynomial of a single variable.
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On Newton's method

TRU Mathematics, 1986
The author has investigated the differential calculus in a linear space whose convergence structure is defined by neighborhoods of the origin, that are not necessarily symmetric. One example of such spaces is the set of all real numbers, where neighborhoods of a point x are \([x,x+\epsilon)\) for \(\epsilon >0\). This space is nonmetrizable.
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Improvements of the Newton–Raphson method

Journal of Computational and Applied Mathematics, 2022
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An acceleration of the continuous Newton’s method

Journal of Computational and Applied Mathematics, 2019
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José M. Gutiérrez 0001, M. A. Hernández-Verón   +1 more
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On Newton's method for polynomials

27th Annual Symposium on Foundations of Computer Science (sfcs 1986), 1986
Let Pd be the set of polynomials over the complex numbers of degree d with all its roots in the unit ball. For f ∈ Pd, let Γf be the set of points for which Newton's method converges to a root, and let Af ≡ |Γf ∩ B2(O)|/|B2(O)|, i.e. the density of Γf in the ball of radius 2. For each d we consider Ad, the worst-case density Af for f ∈ Pd.
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