Two modifications of efficient newton-type iterative method and two variants of Super-Halley’s method for solving nonlinear equations

2019 ◽  
Vol 19 (1) ◽  
pp. 13-22
Author(s):  
Yunhong Hu ◽  
Liang Fang
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Halley’S Method ◽  
Halley's Method

scholarly journals A note on the convergence of Halley's method for solving operator equations

1995 ◽  
Vol 37 (1) ◽  
pp. 16-25 ◽  
Author(s):  
Shiming Zheng ◽  
Desmond Robbie
Keyword(s):  
Nonlinear Equations ◽  
Operator Equations ◽  
Halley’S Method ◽  
Halley's Method

AbstractHalley's method is a famous iteration for solving nonlinear equations. Some Kantorovich-like theorems have been given. The purpose of this note is to relax the region conditions and give another Kantorovich-like theorem for operator equations.

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.

An iterative method for the computation of the solutions of nonlinear equations

CALCOLO ◽  
1999 ◽  
Vol 36 (1) ◽  
pp. 17-34 ◽  
Author(s):  
Francesco Costabile ◽  
Maria Italia Gualtieri ◽  
Stefano Serra Capizzano
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations
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