Accelerating convergence of the globalized Newton method to critical solutions of nonlinear equations

2020 ◽  
Author(s):  
A. Fischer ◽  
A. F. Izmailov ◽  
M. V. Solodov
Keyword(s):  
Nonlinear Equations ◽  
Newton Method ◽  
Critical Solutions

scholarly journals Metode Iterasi Tiga Langkah untuk Menyelesaikan Persamaan NonLinear dengan Menggunakan Matlab

2019 ◽  
Vol 4 (2) ◽  
pp. 34
Author(s):  
Deasy Wahyuni ◽  
Elisawati Elisawati
Keyword(s):  
Numerical Simulations ◽  
Nonlinear Equations ◽  
Newton Method ◽  
Iteration Method ◽  
Newton's Method ◽  
Order Of Convergence ◽  
Higher Order ◽  
Convergence Order ◽  
Matlab Program ◽  
Analytical Results

Newton method is one of the most frequently used methods to find solutions to the roots of nonlinear equations. Along with the development of science, Newton's method has undergone various modifications. One of them is the hasanov method and the newton method variant (vmn), with a higher order of convergence. In this journal focuses on the three-step iteration method in which the order of convergence is higher than the three methods. To find the convergence order of the three-step iteration method requires a program that can support the analytical results of both methods. One of them using the help of the matlab program. Which will then be compared with numerical simulations also using the matlab program.  Keywords : newton method, newton method variant, Hasanov Method and order of convergence

An efficient fourth order weighted-Newton method for systems of nonlinear equations

2012 ◽  
Vol 62 (2) ◽  
pp. 307-323 ◽  
Author(s):  
Janak Raj Sharma ◽  
Rangan Kumar Guha ◽  
Rajni Sharma
Keyword(s):  
Nonlinear Equations ◽  
Newton Method ◽  
Fourth Order ◽  
Systems Of Nonlinear Equations

Computation of Common Normal Between a Wheelset and Straight Rail at Singular Position

2014 ◽  
Author(s):  
Behrooz Fallahi ◽  
Arjun Kumar Perla ◽  
Andrew Behnke
Keyword(s):  
Coordinate System ◽  
Nonlinear Equations ◽  
Newton Method ◽  
Hybrid Procedure ◽  
Bisection Method ◽  
Parametric Equation ◽  
Wheel Surface ◽  
Special Position ◽  
The Common ◽  
Position And Orientation

Computation of common normal between a pair of wheel and rail surface is an important sub problem in railroad simulations. In this study, it is shown that there are special position and orientation of every wheelset that makes the governing equation for computation of the common normal degenerate. This condition leads to divergence of the Newton’s iterate. To develop a procedure that can successfully compute the common normal between a straight rail and a wheelset, first parametric equation for the rail and wheel surface in track coordinate system is developed. Then four nonlinear equations whose solution is location of common normal are constructed. Three of the equations are used to eliminate three unknown in fourth equation. The resulting equation has only one unknown. A hybrid procedure based on Newton method and bisection method is used to solve the roots of the last equation. The utility of this approach is demonstrated by reporting the common normal for a pair of wheel and rail surface at singular position.

Critical solutions of nonlinear equations: local attraction for Newton-type methods

2017 ◽  
Vol 167 (2) ◽  
pp. 355-379 ◽  
Author(s):  
A. F. Izmailov ◽  
A. S. Kurennoy ◽  
M. V. Solodov
Keyword(s):  
Nonlinear Equations ◽  
Critical Solutions

IMPLIED VOLATILITY FROM ASIAN OPTIONS VIA MONTE CARLO METHODS

2009 ◽  
Vol 12 (02) ◽  
pp. 153-178
Author(s):  
ZHAOJUN YANG ◽  
CHRISTIAN-OLIVER EWALD ◽  
YAJUN XIAO
Keyword(s):  
Monte Carlo ◽  
Nonlinear Equations ◽  
Newton Method ◽  
Monte Carlo Methods ◽  
Implied Volatility ◽  
Asian Options ◽  
Classical Approach ◽  
Fast Computation ◽  
Monte Carlo Techniques ◽  
Logarithmic Derivatives

We discuss how implied volatilities for OTC traded Asian options can be computed by combining Monte Carlo techniques with the Newton method in order to solve nonlinear equations. The method relies on accurate and fast computation of the corresponding vegas of the option. In order to achieve this we propose the use of logarithmic derivatives instead of the classical approach. Our simulations document that the proposed method shows far better results than the classical approach. Furthermore we demonstrate how numerical results can be improved by localization.

scholarly journals Performance analysis of a modified Newton method for parameterized dual fuzzy nonlinear equations and its application

2022 ◽  
pp. 105140
Author(s):  
Ibrahim Mohammed Sulaiman ◽  
Mustafa Mamat ◽  
Maulana Malik ◽  
Kottakkaran Sooppy Nisar ◽  
Ashraf Elfasakhany
Keyword(s):  
Performance Analysis ◽  
Nonlinear Equations ◽  
Newton Method ◽  
Modified Newton Method
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