Abstract
The family of Euler-Halley type methods is extended for sections on Riemannian manifolds. Its convergence criterion is established under the assumption that the sections’ covariant derivatives satisfy a kind of Lipschitz condition. Applications to special cases such as the classical Kantorovich’s type condition, the $\gamma$-condition, Smale’s analysis condition are provided.
Citation
Jin-Hua Wang. "Convergence Criterion of the Family of Euler-Halley Type Methods for Sections on Riemannian Manifolds." Taiwanese J. Math. 14 (6) 2181 - 2201, 2010. https://doi.org/10.11650/twjm/1500406069
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