Convergence and Dynamics of Schröder’s Method for Zeros of Analytic Functions with Unknown Multiplicity
In this paper, we investigate the local convergence of Schröder’s method for finding zeros of analytic functions with unknown multiplicity. Thus, we obtain a convergence theorem that provides exact domains of initial points together with error estimates to ensure the <i>Q</i>-quadratic c...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-01-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/13/2/275 |
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| Summary: | In this paper, we investigate the local convergence of Schröder’s method for finding zeros of analytic functions with unknown multiplicity. Thus, we obtain a convergence theorem that provides exact domains of initial points together with error estimates to ensure the <i>Q</i>-quadratic convergence of Schröder’s method right from the first step. A comparison with the famous Newton’s method, based on the convergence and dynamics when it is applied to some polynomial and non-polynomial equations, is also provided. |
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| ISSN: | 2227-7390 |