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...
| 出版年: | AIP Conference Proceedings |
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| 第一著者: | |
| フォーマット: | Conference paper |
| 言語: | English |
| 出版事項: |
American Institute of Physics Inc.
2024
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| オンライン･アクセス: | https://www.scopus.com/inward/record.uri?eid=2-s2.0-85182564911&doi=10.1063%2f5.0173050&partnerID=40&md5=aa937f6002b5272ba9d1b4ead08077c5 |
| 要約: | 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). |
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| ISSN: | 0094243X |
| DOI: | 10.1063/5.0173050 |