Comparative study of one-point optimal family to find multiple roots / Arman Syahir Afandi

A multiple root is a root with multiplicity, also called a multiple point or repeated root. This topic has become a hot conversation to be studied by the researchers. Based on the previous article, they have developed new methods to find multiple root functions which are by using one-point optimal f...

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Main Author:	Afandi, Arman Syahir
Format:	Thesis
Language:	English
Published:	2023
Subjects:	Analytical methods used in the solution of physical problems
Online Access:	https://ir.uitm.edu.my/id/eprint/96599/1/96599.pdf
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id	my-uitm-ir.96599
record_format	uketd_dc
spelling	my-uitm-ir.965992024-06-09T04:18:14Z Comparative study of one-point optimal family to find multiple roots / Arman Syahir Afandi 2023 Afandi, Arman Syahir Analytical methods used in the solution of physical problems A multiple root is a root with multiplicity, also called a multiple point or repeated root. This topic has become a hot conversation to be studied by the researchers. Based on the previous article, they have developed new methods to find multiple root functions which are by using one-point optimal family second-order based on the weight procedure. It is a term that can refer to a family of iterative functions used to approximate the multiple zeros of nonlinear equations. However, in their study, four functions are used by them to check the efficiency of the method. Therefore, by using Maple 2016, the efficiency of three methods which are modified Newton’s method, and other two methods that proposed by them which are Method 5 and Method 6 can be found. The variables that will be used are six different functions and three different initial guesses for each function. Lastly, the method with the lowest iteration and lowest error will be declared as the best method to find multiple root functions. The result showed that not all multiple root functions can be solved by using all three methods. However, the most efficient methods to find multiple roots are by using modified Newton’s method and Method 5 if and only if its initial guess are close to the exact roots. 2023 Thesis https://ir.uitm.edu.my/id/eprint/96599/ https://ir.uitm.edu.my/id/eprint/96599/1/96599.pdf text en public degree Universiti Teknologi MARA, Terengganu College of Computing, Informatics and Mathematics Salahudin, Nur Atikah
institution	Universiti Teknologi MARA
collection	UiTM Institutional Repository
language	English
advisor	Salahudin, Nur Atikah
topic	Analytical methods used in the solution of physical problems
spellingShingle	Analytical methods used in the solution of physical problems Afandi, Arman Syahir Comparative study of one-point optimal family to find multiple roots / Arman Syahir Afandi
description	A multiple root is a root with multiplicity, also called a multiple point or repeated root. This topic has become a hot conversation to be studied by the researchers. Based on the previous article, they have developed new methods to find multiple root functions which are by using one-point optimal family second-order based on the weight procedure. It is a term that can refer to a family of iterative functions used to approximate the multiple zeros of nonlinear equations. However, in their study, four functions are used by them to check the efficiency of the method. Therefore, by using Maple 2016, the efficiency of three methods which are modified Newton’s method, and other two methods that proposed by them which are Method 5 and Method 6 can be found. The variables that will be used are six different functions and three different initial guesses for each function. Lastly, the method with the lowest iteration and lowest error will be declared as the best method to find multiple root functions. The result showed that not all multiple root functions can be solved by using all three methods. However, the most efficient methods to find multiple roots are by using modified Newton’s method and Method 5 if and only if its initial guess are close to the exact roots.
format	Thesis
qualification_level	Bachelor degree
author	Afandi, Arman Syahir
author_facet	Afandi, Arman Syahir
author_sort	Afandi, Arman Syahir
title	Comparative study of one-point optimal family to find multiple roots / Arman Syahir Afandi
title_short	Comparative study of one-point optimal family to find multiple roots / Arman Syahir Afandi
title_full	Comparative study of one-point optimal family to find multiple roots / Arman Syahir Afandi
title_fullStr	Comparative study of one-point optimal family to find multiple roots / Arman Syahir Afandi
title_full_unstemmed	Comparative study of one-point optimal family to find multiple roots / Arman Syahir Afandi
title_sort	comparative study of one-point optimal family to find multiple roots / arman syahir afandi
granting_institution	Universiti Teknologi MARA, Terengganu
granting_department	College of Computing, Informatics and Mathematics
publishDate	2023
url	https://ir.uitm.edu.my/id/eprint/96599/1/96599.pdf
_version_	1804889999273885696

Comparative study of one-point optimal family to find multiple roots / Arman Syahir Afandi

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