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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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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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2018
Capítulo del libro "Contemporary study of iterative methods: convergence, dynamics and applications"
Magreñán, Á. Alberto +1 more
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Capítulo del libro "Contemporary study of iterative methods: convergence, dynamics and applications"
Magreñán, Á. Alberto +1 more
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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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, 2021 Capítulo del libro "Contemporary study of iterative methods: convergence, dynamics and applications"The center Lipschitz condition is used in this chapter, together with the Lipschitz condition, in order to obtain weaker convergence criteria to ensure ...
Argyros, Ioannis K +1 more
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On an Aitken–Newton type method
Numerical Algorithms, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ion Pavaloiu, Emil Catinas
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A Superquadratic Variant of Newton's Method
SIAM Journal on Numerical Analysis, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Accelerated Convergence in Newton’s Method
SIAM Review, 1996Assume that \(f'(a)\neq 0\), while \(f(a)=f''(a)=\dots=f^{(M-1)}(a)=0\) for some \(M\geq 0\). It is shown that Newton's method has at least order \(M\) in this case. Following an idea of \textit{J. Gerlach} [ibid. 36, No. 2, 272-276 (1994; Zbl 0814.65046)] this observation is used for the construction of higher-order moments for the determination of ...
William F. Ford, James A. Pennline
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An asynchronous parallel newton method
Mathematical Programming, 1988A parallel Newton method is described for the minimization of a twice continuously differentiable uniformly convex function F(x). The algorithm generates a sequence \(\{x_ j\}\) which converges superlinearly to the global minimizer of F(x).
H. Fischer, Klaus Ritter
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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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