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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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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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Newton-Raphson Method to Find the Optimal Ordering

OPSEARCH, 1999
In this paper, we show that the Newton-Raphson method is suitable to locate the optimal ordering time for the inventory model taking account of time value. First, we prove that the sequence constructed from Silver-Meal heuristic will converge. Second, we can take a point near to the limit point as the starting point for the Newton-Raphson method ...
Chu, Time P., Tang, W. H.
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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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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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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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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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Convergence of the Newton-Raphson Method For Arbitary Polynomials

The Mathematical Gazette, 1964
Readers may be interested in an elementary exposition of the convergence properties of the sequence of iterates obtained by applying the Newton-Raphson process to an arbitrary polynomial. The coefficients of the polynomial may be real or complex. By restricting attention to polynomials we will give some precise results using the least possible analysis,
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