Kantorovich’s Theorem on Mann’s Iteration Method in Riemannian Manifold

Abstract

Convergence analysis of Mann’s iteration method using Kantorovich’s theorem in the context of connected and complete Riemannian manifolds has been examined in this paper. We also provide an algorithm for Mann’s method to find a singularity in a two dimensional sphere \(S^2\). Finally, we provide an example that shows the better convergence result of Mann’s method in comparison to that of Newton’s method.