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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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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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Newton Raphson Method for Matrix Completion

SSRN Electronic Journal
This paper proposes to use Newton-Raphson/Fisher Scoring iteration to debias/refine initial estimator of matrix completion. We prove that as long as the initial consistent estimator satisfies some loose convergence rate in Frobenius norm, we can get sharp convergence rates of the estimated factors and loadings after just one Newton-Raphson iteration ...
Liangjun Su, Fa Wang
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The Newton-Raphson Nonlinear Optimization Method

2003
Abstract Serious cash flow models used in structured finance are generally required to solve systems of nonlinear equations that stem either from nonlinear regression analysis or from an ad hoc asset-behavior model. Commercial packages exist to solve most nonlinear systems, but integrating them smoothly into a structured analysis code ...
Sylvain Raynes, Ann Rutledge
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Generalized Newton-Raphson method (GNR)

International journal of mathematical sciences, 2012
We present a new method for solving a non-linear equation f(x)=0. The presented method is quadratically convergent, it converges faster than the classical Newton-Raphson method and the Newton- Raphson method appears as the limiting case of the presented method.
Sandrić, Nikola, Viher, Radimir
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