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A family of modified Newton iteration method for solving nonlinear algebraic equations

Luc Xuan Nghiem 1, *
Hieu Nhu Nguyen 2
  1. Thang Long High School, Hanoi, Vietnam
  2. Institute of Mechanics, Vietnam Academy of Science and Technology, VAST
Correspondence to: Luc Xuan Nghiem, Thang Long High School, Hanoi, Vietnam. Email: Nghiado@sci.edu.vn.
Volume & Issue: Vol. 20 No. K2 (2017) | Page No.: 34-41 | DOI: 10.32508/stdj.v20iK2.446
Published: 2017-06-30

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Copyright The Author(s) 2023. This article is published with open access by Vietnam National University, Ho Chi Minh city, Vietnam. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0) which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited. 

Abstract

In this study, a modified Newton iteration version for solving nonlinear algebraic equations is formulated using a correction function derived from convergence order condition of iteration. If the second order of convergence is selected, we get a family of the modified Newton iteration method. Several forms of the correction function are proposed in checking the effectiveness and accuracy of the present iteration method. For illustration, approximate solutions of four examples of nonlinear algebraic equations are obtained and then compared with those obtained from the classical Newton iteration method.

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