Convergence Criterion of the Family of Euler-Halley Type Methods for Sections on Riemannian Manifolds

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.