Solution for divergence problem of the Halley method in solving nonlinear equations using homotopy continuation method

Solution for divergence problem of the Halley method in solving nonlinear equations using homotopy continuation method

It is known that the Halley method will diverge if an initial value is not properly chosen, while the homotopy continuation method (HCM) is a global method that is not sensitive to the initial values. As a result, when the Halley method is associated with the HCM, the divergence problem of the Halle...

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Published in:AIP Conference Proceedings
Main Author: Tahir H.M.; Nor H.M.; Nasir M.A.S.; Bakar S.A.
Format: Conference paper
Language:English
Published: American Institute of Physics Inc. 2024
Online Access:https://www.scopus.com/inward/record.uri?eid=2-s2.0-85182564911&doi=10.1063%2f5.0173050&partnerID=40&md5=aa937f6002b5272ba9d1b4ead08077c5
id 2-s2.0-85182564911
spelling 2-s2.0-85182564911
Tahir H.M.; Nor H.M.; Nasir M.A.S.; Bakar S.A.
Solution for divergence problem of the Halley method in solving nonlinear equations using homotopy continuation method
2024
AIP Conference Proceedings
2905
1
10.1063/5.0173050
https://www.scopus.com/inward/record.uri?eid=2-s2.0-85182564911&doi=10.1063%2f5.0173050&partnerID=40&md5=aa937f6002b5272ba9d1b4ead08077c5
It is known that the Halley method will diverge if an initial value is not properly chosen, while the homotopy continuation method (HCM) is a global method that is not sensitive to the initial values. As a result, when the Halley method is associated with the HCM, the divergence problem of the Halley method can be solved. Furthermore, it can increase the performance of the Halley method. In this paper, the proposed method Halley-HCM method was developed and applied to solve a single polynomial and a system of nonlinear equations. The results show that the Halley-HCM method outperforms the Halley method. © 2024 Author(s).
American Institute of Physics Inc.
0094243X
English
Conference paper
author Tahir H.M.; Nor H.M.; Nasir M.A.S.; Bakar S.A.
spellingShingle Tahir H.M.; Nor H.M.; Nasir M.A.S.; Bakar S.A.
Solution for divergence problem of the Halley method in solving nonlinear equations using homotopy continuation method
author_facet Tahir H.M.; Nor H.M.; Nasir M.A.S.; Bakar S.A.
author_sort Tahir H.M.; Nor H.M.; Nasir M.A.S.; Bakar S.A.
title Solution for divergence problem of the Halley method in solving nonlinear equations using homotopy continuation method
title_short Solution for divergence problem of the Halley method in solving nonlinear equations using homotopy continuation method
title_full Solution for divergence problem of the Halley method in solving nonlinear equations using homotopy continuation method
title_fullStr Solution for divergence problem of the Halley method in solving nonlinear equations using homotopy continuation method
title_full_unstemmed Solution for divergence problem of the Halley method in solving nonlinear equations using homotopy continuation method
title_sort Solution for divergence problem of the Halley method in solving nonlinear equations using homotopy continuation method
publishDate 2024
container_title AIP Conference Proceedings
container_volume 2905
container_issue 1
doi_str_mv 10.1063/5.0173050
url https://www.scopus.com/inward/record.uri?eid=2-s2.0-85182564911&doi=10.1063%2f5.0173050&partnerID=40&md5=aa937f6002b5272ba9d1b4ead08077c5
description It is known that the Halley method will diverge if an initial value is not properly chosen, while the homotopy continuation method (HCM) is a global method that is not sensitive to the initial values. As a result, when the Halley method is associated with the HCM, the divergence problem of the Halley method can be solved. Furthermore, it can increase the performance of the Halley method. In this paper, the proposed method Halley-HCM method was developed and applied to solve a single polynomial and a system of nonlinear equations. The results show that the Halley-HCM method outperforms the Halley method. © 2024 Author(s).
publisher American Institute of Physics Inc.
issn 0094243X
language English
format Conference paper
accesstype
record_format scopus
collection Scopus
_version_ 1809677883305623552

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