Results 61 to 70 of about 39,786 (175)
On the Distance to a Root of Polynomials
Abstract and Applied Analysis, 2011 In 2002, Dierk Schleicher gave an explicit estimate of an upper bound for the number of iterations of Newton's method it takes to find all roots of polynomials with prescribed precision. In this paper, we provide a method to improve the upper bound given
Somjate Chaiya
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An improved Newton iteration for the generalized inverse of a matrix, with applications [PDF]
The purpose here is to clarify and illustrate the potential for the use of variants of Newton's method of solving problems of practical interest on highly personal computers.
Pan, Victor, Schreiber, Robert
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Newton’s Method for the Matrix Nonsingular Square Root
Journal of Applied Mathematics, 2014 Two new algorithms are proposed to compute the nonsingular square root of a matrix A. Convergence theorems and stability analysis for these new algorithms are given. Numerical results show that these new algorithms are feasible and effective.
Chun-Mei Li, Shu-Qian Shen
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Attracting Orbits in Newton's Method [PDF]
Transactions of the American Mathematical Society, 1986 It is well known that the dynamical system generated by Newton’s Method applied to a real polynomial with all of its roots real has no periodic attractors other than the fixed points at the roots of the polynomial. This paper studies the effect on Newton’s Method of roots of a polynomial "going complex".
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Newton's method for stochastic functional differential equations
Electronic Journal of Differential Equations, 2012 In this article, we apply Newton's method to stochastic functional differential equations. The first part concerns a first-order convergence. We formulate a Gronwall-type inequality which plays an important role in the proof of the convergence theorem
Monika Wrzosek
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AIP Advances, 2014 In this paper, an implicit logarithmic finite difference method (I-LFDM) is implemented for the numerical solution of one dimensional coupled nonlinear Burgers’ equation.
Vineet K. Srivastava +3 more
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Assessing the benefits of approximately exact step sizes for Picard and Newton solver in simulating ice flow (FEniCS-full-Stokes v.1.3.2) [PDF]
Geoscientific Model DevelopmentSolving the momentum balance is the computationally expensive part of simulating the evolution of ice sheets. The momentum balance is described by the nonlinear full-Stokes equations, which are solved iteratively. We use the Picard iteration and Newton's
N. Schmidt +4 more
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Newton's Method in Banach Spaces [PDF]
Proceedings of the American Mathematical Society, 1955 1. G. N. Watson, A treatise on the theory of Bessel functions, 2d ed., Cambridge University Press, 1944. 2. K. M. Siegel, An inequality involving Bessel functions of argument nearly equal to their order, Proc. Amer. Math. Soc., vol. 4 (1953) pp. 858-859. 3. K. M. Siegel and F. B.
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Newton’s method and symbolic dynamics [PDF]
Proceedings of the American Mathematical Society, 1984 The starting point of the paper is a result by B. Barna stating the convergence of Newton's method to a root of a polynomial, except for a set of initial points homeomorphic to a Cantor set. The assumptions of Barna's theorem are that: (1) the polynomial has degree at least four; (2) all the roots are real, distinct, and simple.
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Relationship between the inexact Newton method and the continuous analogy of Newton's method
Journal of Numerical Analysis and Approximation Theory, 2011 In this paper we propose two new strategies to determine the forcing terms that allow one to improve the efficiency and robustness of the inexact Newton method.
T. Zhanlav +2 more
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