Science and Education Publishing
American Journal of Numerical Analysis
2328-7292
2
4
2014
05
09
A Modification of Newton Method with Third-Order Convergence
98
101
EN
Gentian
Zavalani
Faculty of Mathematics and Physics Engineering Polytechnic University of Tirana, Albania
AJNA2014241
10.12691/ajna-2-4-1
2014
04
18
2014
05
04
2014
05
09
In this paper, we present a new modification of Newton method for solving non-linear equations. Analysis of convergence shows that the new method is cubically convergent. Per iteration the new method requires two evaluations of the function and one evaluation of its first derivative. Thus, the new method is preferable if the computational costs of the first derivative are equal or more than those of the function itself. Finally, we give some numerical examples to demonstrate our method is more efficient than other classical iterative methods.