Results 21 to 30 of about 10,998,730 (181)
Majorizing sequences for Newton's method from initial value problems [PDF]
, 2012 The most restrictive condition used by Kantorovich for proving the semilocal convergence of Newton's method in Banach spaces is relaxed in this paper, providing we can guarantee the semilocal convergence in situations that Kantorovich cannot.
Hernández, null [0000-0001-5478-2958] +2 more
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Computers & Mathematics with Applications, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Owe Axelsson, Stanislav Sysala
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Chaotic Convergence of Newton’s method
IEEE Transactions on Signal Processing, 2023 <p>Newton's method is considered to be unstable, or worse, chaotic. In this manuscript we show the source of this instability, and present a method to fix the probelm.</p> <p>We also investigate the eigen roots of a modified black-body radiation formula, that seems to explain a connection to quantum mechanics.
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WIREs Computational Statistics, 2010 AbstractNewton's method is one of the most powerful techniques for solving systems of nonlinear equations and minimizing functions. It is easy to implement and has a provably fast rate of convergence under fairly mild assumptions. Because of these and other nice properties, Newton's method is at the heart of many solution techniques used to solve real ...
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Newton's method in Riemannian manifolds
Journal of Numerical Analysis and Approximation Theory, 2008 Using more precise majorizing sequences than before [1], [8], and under the same computational cost, we provide a finer semilocal convergence analysis of Newton's method in Riemannian manifolds with the following advantages: larger convergence domain ...
Ioannis K. Argyros
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Newton's Method in Mixed Precision
SIAM Review, 2022 Abstract: We investigate the use of reduced precision arithmetic to solve the linear equation for the Newton step. If one neglects the backward error in the linear solve, then well-known convergence theory implies that using single precision in the linear solve has very little negative effect on the nonlinear convergence rate.
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Accelerated convergence in Newton's method for approximating square roots [PDF]
, 2005 In this paper, we construct a modification of Newton's method to accelerate the convergence of this method to the approximation of the positive square root of a positive real number.
Romero, N. [0000-0002-0653-560X] +3 more
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Newton's Method for Solving Hilfer Fractional Volterra-Fredholm Integro Differential Equations [PDF]
Sahand Communications in Mathematical AnalysisIn this paper, we apply Newton's method to solve a class of integro-differential equations of the Volterra-Fredholm type with nonlocal characteristics, involving almost sectorial operators and Hilfer fractional derivatives.
karim Ivaz, Ismael Alassadi
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POST-PEAK RESPONSE AUTOMATIC SOLUTIONS IN STRUCTURAL ENGINEERING PROBLEMS – A REVIEW
Mağallaẗ Al-kūfaẗ Al-handasiyyaẗ, 2021 The ill-condition of stiffness matrix at the unstable region for example at the strain-softening region, the load control method will not be valid to give the solution therefore the displacement control method is essential to use. The stiffness matrix is
Husain K. Jarallah
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On the convergence of newton's method
Journal of Complexity, 1989 Sei \(P_ d\) die Menge aller Polynome von Grad d mit komplexen Koeffizienten, deren Nullstellen in der Einheitskreisscheibe liegen. Sei ferner \(\Gamma_ f\) die Menge aller Startpunkte für die das Newtonverfahren zur Lösung \(f(z)=0\) konvergiert. Seien \(B_ 2(0)\) die Kreisscheibe um 0 vom Radius 2, \(A_ f=\mu (\Gamma_ f\cap B_ 2(0))/\mu (B_ 2(0 ...
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