Chebyshev-Halley's method on Riemannian manifolds (Q1696429)
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scientific article; zbMATH DE number 6838769
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Chebyshev-Halley's method on Riemannian manifolds |
scientific article; zbMATH DE number 6838769 |
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Chebyshev-Halley's method on Riemannian manifolds (English)
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14 February 2018
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The authors extend previous results due to \textit{I. K. Argyros} [Korean J. Comput. Appl. Math. 4, No. 1, 83--107 (1997; Zbl 0915.65045)], which require an evaluation of the second Fréchet derivative at each step, to the context of complete Riemannian manifolds, and present a new method which generalizes the important Newton and Chebyshev-Halley methods. These results give them the possibility to study the problem of finding singular points of vector fields on Riemannian manifolds.
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Riemannian manifolds
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Kantorovich-type conditions
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Newton and Chebyshev-Halley's methods
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