Title: A globally convergent interval Newton's method for computing and bounding real roots of a function with one variable

Authors: Ismail Bin Mohd; Yosza Bin Dasril

Addresses: International Journal of KALAM, Lot 3116 Jalan Pantai, Kampung Pengkalan Maras, Mengabang Telipot, 21030 Kuala Terengganu, Malaysia ' Faculty of Technology Management and Business, Universiti Tun Hussein Onn Malaysia, Batu Pahat 86400 Johor, Malaysia

Abstract: It is known that Newton's method is locally convergent, involves errors in numerical computations, and requires an initial guess point for calculating. This initial guess point should be closed enough to the root or zeros otherwise this method fails to converge to the desired root. The method of interval mathematics should overcome these issues and be used to make Newton's method as globally convergent. This paper shows how to use interval mathematics for computing and bounding the simple and multiple roots of multimodal functions. It shows how to solve the problem when zero is in the given interval. The numerical computations for the two examples show the ability of newly proposed methods and satisfactory computational behaviour and convince us that Newton's method is able to solve nonlinear problems statement.

Keywords: interval mathematics? global convergence? root finding? Newton's method? nonlinear? Alefeld's method? algorithm.

DOI: 10.1504/IJMOR.2021.120103

International Journal of Mathematics in Operational Research, 2021 Vol.20 No.4, pp.521 - 547

Received: 19 Jun 2020
Accepted: 05 Sep 2020

Published online: 07 Jan 2022 *

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