scholarly journals Ball convergence theorems for eighth-order variants of Newton’s method under weak conditions

2015 ◽  
Vol 4 (2) ◽  
pp. 81-90
Author(s):  
Ioannis K. Argyros ◽  
Santhosh George
Keyword(s):  
Newton’S Method ◽  
Newton's Method ◽  
Eighth Order ◽  
Convergence Theorems ◽  
Ball Convergence

scholarly journals Some New Higher Order Weighted Newton Methods for Solving Nonlinear Equation with Applications

2019 ◽  
Vol 24 (2) ◽  
pp. 59
Author(s):  
Parimala Sivakumar ◽  
Jayakumar Jayaraman
Keyword(s):  
Fourth Order ◽  
Newton’S Method ◽  
Newton's Method ◽  
Efficiency Index ◽  
Higher Order ◽  
Function Technique ◽  
Function Evaluation ◽  
Step Method ◽  
Eighth Order ◽  
Additional Function

Three new iterative methods for solving scalar nonlinear equations using weight function technique are presented. The first one is a two-step fifth order method with four function evaluations which is improved from a two-step Newton’s method having same number of function evaluations. By this, the efficiency index of the new method is improved from 1.414 to 1.495. The second one is a three step method with one additional function evaluation producing eighth order accuracy with efficiency index 1.516. The last one is a new fourth order optimal two-step method with efficiency index 1.587. All these three methods are better than Newton’s method and many other equivalent higher order methods. Convergence analyses are established so that these methods have fifth, eighth and fourth order respectively. Numerical examples ascertain that the proposed methods are efficient and demonstrate better performance when compared to some equivalent and optimal methods. Seven application problems are solved to illustrate the efficiency and performance of the proposed methods.

scholarly journals Newton’s Method for the Matrix Nonsingular Square Root

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Chun-Mei Li ◽  
Shu-Qian Shen
Keyword(s):  
Stability Analysis ◽  
Newton’S Method ◽  
Newton's Method ◽  
Numerical Results ◽  
Square Root ◽  
Convergence Theorems ◽  
The Matrix ◽  
New Algorithms

Two new algorithms are proposed to compute the nonsingular square root of a matrixA. Convergence theorems and stability analysis for these new algorithms are given. Numerical results show that these new algorithms are feasible and effective.

scholarly journals Improved Fast ICA Algorithm Using Eighth-Order Newton's Method

2013 ◽  
Vol 6 (10) ◽  
pp. 1794-1798
Author(s):  
Tahir Ahmad ◽  
Norma Alias ◽  
Mahdi Ghanbari ◽  
Mohammad Askaripour
Keyword(s):  
Newton’S Method ◽  
Newton's Method ◽  
Eighth Order ◽  
Ica Algorithm

scholarly journals Extended convergence of Gauss-Newton’s method and uniqueness of the solution

2018 ◽  
Vol 34 (2) ◽  
pp. 135-142
Author(s):  
IOANNIS K. ARGYROS ◽  
◽  
YEOL JE CHO ◽  
SANTHOSH GEORGE ◽  
◽  
...  
Keyword(s):  
Least Squares ◽  
Convergence Analysis ◽  
Newton’S Method ◽  
Newton's Method ◽  
Nonlinear Least Squares ◽  
Lipschitz Functions ◽  
New Technique ◽  
Least Squares Problems ◽  
Uniqueness Of The Solution ◽  
Ball Convergence

The aim of this paper is to extend the applicability of the Gauss-Newton’s method for solving nonlinear least squares problems using our new idea of restricted convergence domains. The new technique uses tighter Lipschitz functions than in earlier papers leading to a tighter ball convergence analysis.

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