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S. Weerakoon, T.G.I. Fernando, A variant of Newton’s method with accelerated third- order convergence, Appl. Math. Lett. 13 (2000) 87-93.

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Article

A Modification of Newton Method with Third-Order Convergence

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


American Journal of Numerical Analysis. 2014, Vol. 2 No. 4, 98-101
DOI: 10.12691/ajna-2-4-1
Copyright © 2014 Science and Education Publishing

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.

Correspondence to: Gentian  Zavalani, Faculty of Mathematics and Physics Engineering Polytechnic University of Tirana, Albania. Email: zavalanigentian@hotmail.com

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.

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