scholarly journals Generalized Simpson-Newton's Method for Solving Nonlinear Equations with Cubic Convergence

2013 ◽  
Vol 7 (5) ◽  
pp. 58-61
Author(s):  
J. Jayakumar ◽  
Keyword(s):  
Nonlinear Equations ◽  
Newton’S Method ◽  
Newton's Method ◽  
Cubic Convergence

An Efficient Sixth-Order Convergent Newton-Type Iterative Method for Nonlinear Equations

2012 ◽  
Vol 220-223 ◽  
pp. 2585-2588
Author(s):  
Zhong Yong Hu ◽  
Fang Liang ◽  
Lian Zhong Li ◽  
Rui Chen
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Newton’S Method ◽  
Newton's Method ◽  
Efficiency Index ◽  
Sixth Order ◽  
Type Method ◽  
Second Derivatives ◽  
Better Than

In this paper, we present a modified sixth order convergent Newton-type method for solving nonlinear equations. It is free from second derivatives, and requires three evaluations of the functions and two evaluations of derivatives per iteration. Hence the efficiency index of the presented method is 1.43097 which is better than that of classical Newton’s method 1.41421. Several results are given to illustrate the advantage and efficiency the algorithm.

scholarly journals A Hybrid Approach for Solving Systems of Nonlinear Equations Using Harris Hawks Optimization and Newton’s Method

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Rami Sihwail ◽  
Obadah Said Solaiman ◽  
Khairuddin Omar ◽  
Khairul Akram Zainol Ariffin ◽  
Mohammed Alswaitti ◽  
...  
Keyword(s):  
Nonlinear Equations ◽  
Newton’S Method ◽  
Newton's Method ◽  
Hybrid Approach ◽  
Systems Of Nonlinear Equations

scholarly journals Modified Newton’s method for systems of nonlinear equations with singular Jacobian

2009 ◽  
Vol 224 (1) ◽  
pp. 77-83 ◽  
Author(s):  
José L. Hueso ◽  
Eulalia Martínez ◽  
Juan R. Torregrosa
Keyword(s):  
Nonlinear Equations ◽  
Newton’S Method ◽  
Newton's Method ◽  
Systems Of Nonlinear Equations ◽  
Modified Newton’S Method ◽  
Singular Jacobian

Quantum Newton’s Method for Solving the System of Nonlinear Equations

SPIN ◽  
2021 ◽  
pp. 2140004
Author(s):  
Cheng Xue ◽  
Yuchun Wu ◽  
Guoping Guo
Keyword(s):  
Quantum Computing ◽  
Nonlinear Equations ◽  
Newton’S Method ◽  
Newton's Method ◽  
Linear Equations ◽  
Data Conversion ◽  
System Of Nonlinear Equations ◽  
Dimensional System ◽  
System Of Linear Equations ◽  
Whole Process

While quantum computing provides an exponential advantage in solving the system of linear equations, there is little work to solve the system of nonlinear equations with quantum computing. We propose quantum Newton’s method (QNM) for solving [Formula: see text]-dimensional system of nonlinear equations based on Newton’s method. In QNM, we solve the system of linear equations in each iteration of Newton’s method with quantum linear system solver. We use a specific quantum data structure and [Formula: see text] tomography with sample error [Formula: see text] to implement the classical-quantum data conversion process between the two iterations of QNM, thereby constructing the whole process of QNM. The complexity of QNM in each iteration is [Formula: see text]. Through numerical simulation, we find that when [Formula: see text], QNM is still effective, so the complexity of QNM is sublinear with [Formula: see text], which provides quantum advantage compared with the optimal classical algorithm.

Optimal Design With a Monomial-Based Version of Newton’s Method

1991 ◽  
Author(s):  
Scott A. Burns
Keyword(s):  
Optimal Design ◽  
Design Optimization ◽  
Engineering Design ◽  
Nonlinear Equations ◽  
Newton’S Method ◽  
Newton's Method ◽  
Geometric Mean ◽  
System Of Nonlinear Equations ◽  
Engineering Design Optimization

Abstract A monomial-based method for solving systems of algebraic nonlinear equations is presented. The method uses the arithmetic-geometric mean inequality to construct a system of monomial equations that approximates the system of nonlinear equations. This “monomial method” is closely related to Newton’s method, yet exhibits many special properties not shared by Newton’s method that enhance performance. These special properties are discussed in relation to engineering design optimization.

On Newton's Method for Solving Nonlinear Equations and Function Splitting

2011 ◽  
Vol 4 (1) ◽  
pp. 53-67
Author(s):  
Ioannis K. Argyros & Saïd Hilout
Keyword(s):  
Nonlinear Equations ◽  
Newton’S Method ◽  
Newton's Method ◽  
And Function

An efficient without direct function evaluations Newton's method for solving systems of nonlinear equations

2019 ◽  
Vol 13 (1) ◽  
pp. 11-23
Author(s):  
Eleftheria N. Malihoutsaki ◽  
Theodoula N. Grapsa
Keyword(s):  
Nonlinear Equations ◽  
Newton’S Method ◽  
Newton's Method ◽  
Systems Of Nonlinear Equations ◽  
Direct Function

A variant of Newton’s method based on Simpson’s three-eighths rule for nonlinear equations

2018 ◽  
Vol 79 ◽  
pp. 1-5 ◽  
Author(s):  
Jen-Yuan Chen ◽  
David R. Kincaid ◽  
Bei-Ru Lin
Keyword(s):  
Nonlinear Equations ◽  
Newton’S Method ◽  
Newton's Method

Newton’s method for solving a system of fuzzy nonlinear equations

2006 ◽  
Vol 175 (2) ◽  
pp. 1189-1199 ◽  
Author(s):  
S. Abbasbandy ◽  
R. Ezzati
Keyword(s):  
Nonlinear Equations ◽  
Newton’S Method ◽  
Newton's Method
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