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Improvements of Modified Newton-Raphson Method

Improvements of Modified Newton-Raphson Method
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Improvements of the Newton–Raphson method

Journal of Computational and Applied Mathematics, 2022
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Kim-Hung Pho
exaly   +2 more sources

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
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THE NEWTON–RAPHSON METHOD AND ADAPTIVE ODE SOLVERS [PDF]

Fractals, 2011
The Newton–Raphson method for solving nonlinear equations f(x) = 0 in ℝn is discussed within the context of ordinary differential equations. This framework makes it possible to reformulate the scheme by means of an adaptive step size control procedure that aims at reducing the chaotic behavior of the original method without losing the quadratic ...
SCHNEEBELI, HANS RUDOLF, WIHLER, THOMAS P.   +1 more
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A generalized Newton-Raphson method using curvature

Communications in Numerical Methods in Engineering, 1995
AbstractA numerical method for finding the roots of any function is developed. This method considers a circle using the concept of curvature instead of the tangential line in the Newton‐Raphson method. The compared results between the proposed method and the Newton‐Raphson method are listed.
Lee, IW Lee, In Won, JUNG, GH JUNG, GH
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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
exaly   +3 more sources

Newton–Raphson Method

2010
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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 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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