Chandresh Prasad, Pradip Kumar Parida

Semilocal Convergence Analysis of the third order Newton-like method in Riemannian manifolds

Introduction

Semilocal convergence analysis of the third order newton-like method in riemannian manifolds. Semilocal convergence analysis for a third-order Newton-like method in Riemannian manifolds. We cover Lipschitz continuity, derive convergence order, and present a numerical example.

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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