Results 141 to 150 of about 7,608 (193)

Randomized Newton-Raphson

Applied Numerical Mathematics, 1990
Let g: \(R^ 1\to R^ 1\) be a differentiable function. For the numerical solutions of the equation \(g(x)=0\) a randomized Newton process of the form \(X_{k+1}=x_ k-(g(x_ k)+Z_{1,k})/(g'(x_ k)+Z_{2,k}),\quad k=0,1,...,\) is considered where \(Z_{1,k}\), \(Z_{2,k}\) are mutually independent random variables with controllable densities and hence \(\{X_ k\}
Joseph, G., Levine, A., Liukkonen, J.
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A geometric Newton–Raphson strategy

Computer Aided Geometric Design, 2001
In the standard Newton-Raphson algorithm for solving nonlinear equations, a new guess is computed by solving a linear approximation of the problem at the current guess. A similar, very effective strategy is proposed here for solving geometric problems (e.g., finding intersections) on general plane curves.
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ON NEWTON-RAPHSON METHOD [PDF]

Journal of Information Systems and Operations Management, 2011
Recent versions of the well-known Newton-Raphson method for solving algebraic equations are presented. First of these is the method given by J. H. He in 2003. He reduces the problem to solving a second degree polynomial equation. However He’s method is not applicable when this equation has complex roots. In 2008, D. Wei, J. Wu and M.
Mircea Cirnu, Irina Badralexi
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The Newton‐Raphson method

International Journal of Mathematical Education in Science and Technology, 1995
We start with an historical introduction, and then give an overview of the most important concepts and properties of general iterative methods to solve nonlinear equations. Then we study extensively the Newton‐Raphson method, investigating different sufficient conditions for the Newton‐Raphson method to converge. Finally we look at systems of nonlinear
Johan Verbeke, Ronald Cools
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A generalization of Newton‐Raphson

International Journal of Mathematical Education in Science and Technology, 1984
It is shown that the Newton‐Raphson iteration for nonlinear equations can be considered as a member of a general one‐parameter family of second‐order methods. Variation of the parameter can greatly increase the speed of convergence, and a criterion for choosing the optimal parameter is derived.
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A faster modified newton-raphson iteration

Computer Methods in Applied Mechanics and Engineering, 1979
Abstract The paper describes an accelerated modified Newton-Raphson iteration in which the iterative deflection change is a scalar times the previous iterative change plus a further scalar times the usual unaccelerated change. These scalars are automatically recalculated at each iteration.
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A note on starting the Newton-Raphson method

Communications of the ACM, 1964
Determination of a suitable initial estimate for a root of an equation ƒ( x ) = 0 by means of computing the roots of a sequence of related equations is described.
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Extended Newton-Raphson Method

2016
In Chap. 7, we have seen that overdetermined nonlinear systems are common in geodetic and geoinformatic applications, that is there are frequently more measurements than it is necessary to determine unknown variables, consequently the number of the variables n is less then the number of the equations m.
Joseph L. Awange, Béla Paláncz
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A stochastic Newton-Raphson method

Journal of Statistical Planning and Inference, 1978
Abstract A stochastic approximation procedure of the Robbins-Monro type is considered. The original idea behind the Newton-Raphson method is used as follows. Given n approximations X 1 ,…, X n with observations Y 1 ,…, Y n , a least squares line is fitted to the points ( X m , Y m ),…, ( X n , Y n ) where m n may ...
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Geometric Newton-Raphson Method

2002
Given an equation y = f (x), the Newton-Raphson method employs successive approximations to determine the roots of the equation f (x) = 0.
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