Resumen de Third-order methods on Riemannian manifolds under Kantorovich conditions

Sergio Amat Plata, Sonia Busquier Sáez, Raúl R. Castro, Sergio Plaza Salinas

• One of the most studied problems in numerical analysis is the approximation of nonlinear equations using iterative methods. In the past years, attention has been paid in studying Newton�s method on manifolds. In this paper, we generalize this study by considering a general class of third-order iterative methods. A characterization of the convergence under Kantorovich type conditions and optimal error estimates is found.