Analysis of Traub’s Method for Cubic Polynomials
The dynamical analysis of Kurchatov’s scheme is extended to Traub’s method. The difference here is that Traub’s method requires two additional starting points. Therefore, the map is three-dimensional instead of 2-D. We obtain a complete description of the dynamical planes and show that the method is...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-01-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/13/2/87 |
| _version_ | 1797298869864759296 |
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| author | Beny Neta |
| author_facet | Beny Neta |
| author_sort | Beny Neta |
| collection | DOAJ |
| description | The dynamical analysis of Kurchatov’s scheme is extended to Traub’s method. The difference here is that Traub’s method requires two additional starting points. Therefore, the map is three-dimensional instead of 2-D. We obtain a complete description of the dynamical planes and show that the method is stable for cubic polynomials. |
| first_indexed | 2024-03-07T22:42:19Z |
| format | Article |
| id | doaj.art-1f6e478661c74c06a788a512ec2c4106 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-07T22:42:19Z |
| publishDate | 2024-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-1f6e478661c74c06a788a512ec2c41062024-02-23T15:07:22ZengMDPI AGAxioms2075-16802024-01-011328710.3390/axioms13020087Analysis of Traub’s Method for Cubic PolynomialsBeny Neta0Department of Applied Mathematics, Naval Postgraduate School, Monterey, CA 93943, USAThe dynamical analysis of Kurchatov’s scheme is extended to Traub’s method. The difference here is that Traub’s method requires two additional starting points. Therefore, the map is three-dimensional instead of 2-D. We obtain a complete description of the dynamical planes and show that the method is stable for cubic polynomials.https://www.mdpi.com/2075-1680/13/2/87nonlinear equationssimple rootsderivative-free methods |
| spellingShingle | Beny Neta Analysis of Traub’s Method for Cubic Polynomials Axioms nonlinear equations simple roots derivative-free methods |
| title | Analysis of Traub’s Method for Cubic Polynomials |
| title_full | Analysis of Traub’s Method for Cubic Polynomials |
| title_fullStr | Analysis of Traub’s Method for Cubic Polynomials |
| title_full_unstemmed | Analysis of Traub’s Method for Cubic Polynomials |
| title_short | Analysis of Traub’s Method for Cubic Polynomials |
| title_sort | analysis of traub s method for cubic polynomials |
| topic | nonlinear equations simple roots derivative-free methods |
| url | https://www.mdpi.com/2075-1680/13/2/87 |
| work_keys_str_mv | AT benyneta analysisoftraubsmethodforcubicpolynomials |