Version 1
: Received: 21 October 2024 / Approved: 21 October 2024 / Online: 22 October 2024 (07:11:30 CEST)
How to cite:
Yong, L. Research Progress on Newton’s Iterative Methods for Nonlinear Equation. Preprints2024, 2024101642. https://doi.org/10.20944/preprints202410.1642.v1
Yong, L. Research Progress on Newton’s Iterative Methods for Nonlinear Equation. Preprints 2024, 2024101642. https://doi.org/10.20944/preprints202410.1642.v1
Yong, L. Research Progress on Newton’s Iterative Methods for Nonlinear Equation. Preprints2024, 2024101642. https://doi.org/10.20944/preprints202410.1642.v1
APA Style
Yong, L. (2024). Research Progress on Newton’s Iterative Methods for Nonlinear Equation. Preprints. https://doi.org/10.20944/preprints202410.1642.v1
Chicago/Turabian Style
Yong, L. 2024 "Research Progress on Newton’s Iterative Methods for Nonlinear Equation" Preprints. https://doi.org/10.20944/preprints202410.1642.v1
Abstract
Reviewed the research progress of Newton’s iterative methods for nonlinear equation. Convergence with second order, third order, fourth order, fifth order, sixth order, seventh order, eighth order and ninth order Newton’s iterative methods are given in turn, and the efficiency index of these iterative methods are analyzed. Numerical experiments show that the convergence process of the three Newton iterative methods, and the results indicate that the convergence of the higher-order Newton’s method can be well demonstrated only when the initial point is close to the root.
Computer Science and Mathematics, Computational Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.