Results 181 to 190 of about 300,170 (232)

A Modified Newton–Raphson Method

Communications in Numerical Methods in Engineering, 2004
AbstractIn this paper, we propose the following modified Newton–Raphson iteration formulation: In case r=1, the obtained formulation reduces to the Newton–Raphson formulation. The present technique circumvent pitfalls of the Newton–Raphson iteration method. Some examples are illustrated. Copyright © 2004 John Wiley & Sons, Ltd.
Ji-Huan He
exaly   +2 more sources

Improvements of Convergence Characteristics of Newton-Raphson Method for Nonlinear Magnetic Field Analysis [PDF]

IEEE Transactions on Magnetics, 1992
In order to overcome the divergence of the Newton-Raphson iteration in the nonlinear magnetic field analysis, a relaxation factor is introduced and its optimum value is examined. It is shown that the modified Newton-Raphson method proposed exhibits quick
Kazuhiro Muramatsu, T Nakata
exaly   +3 more sources

Newton–Raphson Method

2010
exaly   +2 more sources

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.
openaire   +2 more sources

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.
openaire   +2 more sources

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
openaire  

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
openaire   +1 more source

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.
openaire   +1 more source

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.
openaire   +3 more sources