Semilocal convergence analysis of an eighth order iterative method for solving nonlinear systems
In this paper, the semilocal convergence of the eighth order iterative method is proved in Banach space by using the recursive relation, and the proof process does not need high order derivative. By selecting the appropriate initial point and applying the Lipschitz condition to the first order Fréch...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2023-07-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20231141?viewType=HTML |
| Summary: | In this paper, the semilocal convergence of the eighth order iterative method is proved in Banach space by using the recursive relation, and the proof process does not need high order derivative. By selecting the appropriate initial point and applying the Lipschitz condition to the first order Fréchet derivative in the whole region, the existence and uniqueness domain are obtained. In addition, the theoretical results of semilocal convergence are applied to two nonlinear systems, and satisfactory results are obtained. |
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| ISSN: | 2473-6988 |