Semilocal Convergence Analysis of the third order Newton-like method in Riemannian manifolds
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Abstract
In this paper, we present the semilocal convergence analysis of the third order Newton-like method in Riemannian manifolds. We study the convergence analysis of our method under Lipschitz continuity condition on the first order covariant derivative of a vector field. Using normal coordinates the order of convergence is derived. Finally, a numerical example is given to show the effectiveness of our results.
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