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Variable density and chemical reaction effects on heat and mass transfer of magnetic second-grade nanofluid flow under slip conditions. [PDF]
Benaissa M +8 more
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Design and Experimental Validation of a Piezoelectrically Controlled Micro-Newton Cold-Gas Thruster Head. [PDF]
Zhu X +7 more
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Insomnia Symptoms are Common Among Community Dwelling African Americans Who Report Poor Sleep. [PDF]
Peyrel P +10 more
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Initial Estimate Selection Method in Passive TDOA-Based Iterative Position Estimation Algorithms. [PDF]
Kaczmarek B, Główczyk B, Zieja M.
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GEORCE: a fast new control algorithm for computing geodesics. [PDF]
Rygaard FM, Hauberg S.
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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
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Accelerated Convergence in Newton’s Method
SIAM Review, 1994\textit{G. H. Brown jun.} [Am. Math. Monthly 84, 726-728 (1977; Zbl 0375.65025)] and \textit{G. Alefeld} [ibid. 88, 530-536 (1981; Zbl 0486.65035)] applied Newton's method to \(F(x):= f(x)/\sqrt{f'(x)}\), \(f\) being a real-valued function of a real variable, to solve \(f(x)= 0\) approximately, and thus obtained Halley's method for \(f\).
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Expanding the applicability of Newton’s method and of a robust modified Newton’s method
Applicationes Mathematicae, 2021Summary: 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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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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