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Determining radius of convergence of Newton's method using radius of curvature

In this paper, we propose a method on how to manage the convergence of Newton’s method if its iteration process encounters a local extremum. This idea establishes the osculating circle at a local extremum. It then uses the radius of the osculating circle also known as the radius of the curvature as...

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Main Authors: Pandiya, Ridwan, Mohd, Ismail
Format: Article
Language:English
Published: Penerbit UTM Press 2017
Online Access:http://psasir.upm.edu.my/id/eprint/13432/1/Determining%20radius%20of%20convergence%20of%20Newton%27s%20method%20using%20radius%20of%20curvature.pdf
http://psasir.upm.edu.my/id/eprint/13432/
https://matematika.utm.my/index.php/matematika/article/view/836
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spelling my.upm.eprints.134322018-06-11T08:18:01Z http://psasir.upm.edu.my/id/eprint/13432/ Determining radius of convergence of Newton's method using radius of curvature Pandiya, Ridwan Mohd, Ismail In this paper, we propose a method on how to manage the convergence of Newton’s method if its iteration process encounters a local extremum. This idea establishes the osculating circle at a local extremum. It then uses the radius of the osculating circle also known as the radius of the curvature as an additional number of the local extremum. It then takes that additional number and combines it with the local extremum. This is then used as an initial guess in finding a root near to that local extremum. This paper will provide several examples which demonstrate that our idea is successful and they perform to fulfill the aim of this paper. Penerbit UTM Press 2017 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/13432/1/Determining%20radius%20of%20convergence%20of%20Newton%27s%20method%20using%20radius%20of%20curvature.pdf Pandiya, Ridwan and Mohd, Ismail (2017) Determining radius of convergence of Newton's method using radius of curvature. Matematika, 33 (1). pp. 43-54. ISSN 0127-8274 https://matematika.utm.my/index.php/matematika/article/view/836 10.11113/matematika.v33.n1.836
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
description In this paper, we propose a method on how to manage the convergence of Newton’s method if its iteration process encounters a local extremum. This idea establishes the osculating circle at a local extremum. It then uses the radius of the osculating circle also known as the radius of the curvature as an additional number of the local extremum. It then takes that additional number and combines it with the local extremum. This is then used as an initial guess in finding a root near to that local extremum. This paper will provide several examples which demonstrate that our idea is successful and they perform to fulfill the aim of this paper.
format Article
author Pandiya, Ridwan
Mohd, Ismail
spellingShingle Pandiya, Ridwan
Mohd, Ismail
Determining radius of convergence of Newton's method using radius of curvature
author_facet Pandiya, Ridwan
Mohd, Ismail
author_sort Pandiya, Ridwan
title Determining radius of convergence of Newton's method using radius of curvature
title_short Determining radius of convergence of Newton's method using radius of curvature
title_full Determining radius of convergence of Newton's method using radius of curvature
title_fullStr Determining radius of convergence of Newton's method using radius of curvature
title_full_unstemmed Determining radius of convergence of Newton's method using radius of curvature
title_sort determining radius of convergence of newton's method using radius of curvature
publisher Penerbit UTM Press
publishDate 2017
url http://psasir.upm.edu.my/id/eprint/13432/1/Determining%20radius%20of%20convergence%20of%20Newton%27s%20method%20using%20radius%20of%20curvature.pdf
http://psasir.upm.edu.my/id/eprint/13432/
https://matematika.utm.my/index.php/matematika/article/view/836
_version_ 1643825330057641984
score 13.211869

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