On some Aitken-Steffensen-Halley-type methods for approximating the roots of scalar equations
In this note we extend the Aitken-Steffensen method to the Halley transformation. Under some rather simple assumptions we obtain error bounds for each iteration step; moreover, the convergence order of the iterates is 3, i.e. higher than for the Aitken-Steffensen case.
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| Format: | Article |
| Language: | English |
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Publishing House of the Romanian Academy
2001-08-01
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| Series: | Journal of Numerical Analysis and Approximation Theory |
| Online Access: | https://www.ictp.acad.ro/jnaat/journal/article/view/697 |