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Journal of Applied Mathematics and Computing, 2010
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Argyros, Ioannis K., Hilout, Saïd
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Argyros, Ioannis K., Hilout, Saïd
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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. +2 more
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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. +2 more
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A parameterized Newton method and a quasi-Newton method for nonsmooth equations
Computational Optimization and Applications, 1994Two 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, 1998zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Cores, D., Tapia, R. A.
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GENERALIZATIONS OF NEWTON'S METHOD
Fractals, 2001We 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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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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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, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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An acceleration of the continuous Newton’s method
Journal of Computational and Applied Mathematics, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
José M. Gutiérrez 0001 +1 more
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On Newton's method for polynomials
27th Annual Symposium on Foundations of Computer Science (sfcs 1986), 1986Let 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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The improvements of modified Newton’s method
Applied Mathematics and Computation, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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