Results 151 to 160 of about 7,370 (187)

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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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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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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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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Accelerated Newton–Raphson power flow

European Transactions on Electrical Power, 2011
SUMMARYThis paper introduces the Newton‐like method of modifying the right‐hand‐side vector into the power flow solution. Based on this method, the accelerated Newton–Raphson (ANR) power flow algorithm is proposed. In the proposed algorithm, a constant Jacobian matrix in the correction equations is employed to reduce the computation burden, while the ...
Gan Li, Xiao‐Ping Zhang, Xi‐Fan Wang
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Variable dimension Newton-Raphson method

IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 2000
Summary: The classical Newton-Raphson method is generalized to solve nonsquare and nonlinear problems of size \(m\times n\) with \(m\leq n\). Using this generalized Newton-Raphson method as a core, a new variable dimension Newton-Raphson (VDNR) method is developed.
Ng, S. W., Lee, Y. S.
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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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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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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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An Asynchronous Newton-Raphson Method

1990
We consider a parallel variant of the Newton-Raphson method for unconstrained optimization, which uses as many finite differences of gradients as possible to approximate rows and columns of the inverse Hessian matrix. The method is based on the Gauss-Seidel type of updating for quasi-Newton methods originally proposed by Straeter (1973).
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