A Novel n-Point Newton-Type Root-Finding Method of High Computational Efficiency
A novel Newton-type n-point iterative method with memory is proposed for solving nonlinear equations, which is constructed by the Hermite interpolation. The proposed iterative method with memory reaches the order (2n+2n−1−1+22n+1+22n−2+2n+1)/2 by using n variable parameters. The computational effici...
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| Published in | Mathematics (Basel) Vol. 10; no. 7; p. 1144 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
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Basel
MDPI AG
01.04.2022
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| Abstract | A novel Newton-type n-point iterative method with memory is proposed for solving nonlinear equations, which is constructed by the Hermite interpolation. The proposed iterative method with memory reaches the order (2n+2n−1−1+22n+1+22n−2+2n+1)/2 by using n variable parameters. The computational efficiency of the proposed method is higher than that of the existing Newton-type methods with and without memory. To observe the stability of the proposed method, some complex functions are considered under basins of attraction. Basins of attraction show that the proposed method has better stability and requires a lesser number of iterations than various well-known methods. The numerical results support the theoretical results. |
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| AbstractList | A novel Newton-type n-point iterative method with memory is proposed for solving nonlinear equations, which is constructed by the Hermite interpolation. The proposed iterative method with memory reaches the order ( 2n+2n−1−1+22n+1+22n−2+2n+1 ) /2 by using n variable parameters. The computational efficiency of the proposed method is higher than that of the existing Newton-type methods with and without memory. To observe the stability of the proposed method, some complex functions are considered under basins of attraction. Basins of attraction show that the proposed method has better stability and requires a lesser number of iterations than various well-known methods. The numerical results support the theoretical results. |
| Author | Wang, Xiaofeng |
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| CitedBy_id | crossref_primary_10_1016_j_eswa_2023_119987 crossref_primary_10_1016_j_cam_2023_115096 crossref_primary_10_1177_09544070241265395 |
| Cites_doi | 10.3390/math8071080 10.3390/fractalfract6010046 10.3390/fractalfract6020059 10.1137/100805340 10.1007/s11075-014-9951-8 10.1016/j.cam.2017.07.003 10.1137/1.9780898718898 10.3390/fractalfract6030174 10.3390/sym13050884 10.1145/321850.321860 10.3390/a8030786 10.1137/090758763 10.1016/j.aml.2011.01.002 10.1007/s11075-009-9345-5 10.3390/fractalfract5020027 10.1016/B978-0-12-397013-8.00002-9 10.1016/j.cam.2020.113053 10.3390/fractalfract5010025 10.1007/s10957-011-9929-9 10.1201/9781315153469 10.1016/j.cam.2013.05.013 |
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| SubjectTerms | Approximation Attraction Basins Computational efficiency Computing time Efficiency Interpolation Iterative methods Mathematics Methods nonlinear equation Nonlinear equations Numerical methods optimal convergence order Stability |
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| Title | A Novel n-Point Newton-Type Root-Finding Method of High Computational Efficiency |
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