A fifth-order family of modified Newton methods

1971 ◽  
Vol 11 (4) ◽  
pp. 409-412 ◽  
Author(s):  
Richard F. King
Keyword(s):  
Newton Methods ◽  
Fifth Order ◽  
Modified Newton Methods

Three-Step Method with Fifth-Order Convergence for Nonlinear Equation

2013 ◽  
Vol 846-847 ◽  
pp. 1274-1277
Author(s):  
Ying Peng Zhang ◽  
Li Sun
Keyword(s):  
Nonlinear Equation ◽  
Iterative Method ◽  
Efficiency Index ◽  
Newton Methods ◽  
Order Convergence ◽  
Step Method ◽  
Second Derivatives ◽  
Fifth Order ◽  
Modified Newton Methods ◽  
Better Than

We present a fifth-order iterative method for the solution of nonlinear equation. The new method is based on two ordinary methods, which are modified Newton methods without second derivatives. Its efficiency index is 1.37973 which is better than that of Newton's method. Numerical results show the efficiency of the proposed method.

On modified Newton methods with cubic convergence

2006 ◽  
Vol 176 (1) ◽  
pp. 123-127 ◽  
Author(s):  
Jisheng Kou ◽  
Yitian Li ◽  
Xiuhua Wang
Keyword(s):  
Newton Methods ◽  
Cubic Convergence ◽  
Modified Newton Methods
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