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.
Taiwanese J. Math.
14(6):
2181-2201
(2010).
DOI: 10.11650/twjm/1500406069