A Modification of Newton Method with Third-Order Convergence

Gentian Zavalani^1,

¹Faculty of Mathematics and Physics Engineering Polytechnic University of Tirana, Albania

Cite this paper:
Gentian Zavalani. A Modification of Newton Method with Third-Order Convergence. American Journal of Numerical Analysis. 2014; 2(4):98-101. doi: 10.12691/ajna-2-4-1

Abstract

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.

Keywords:
Newton method third-order convergence non-linear equations iterative method quadrature formulas

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