Third-order methods on Riemannian manifolds under Kantorovich conditions

• Autores: Sergio Amat Plata , Sonia Busquier Sáez , Raúl R. Castro, Sergio Plaza Salinas
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 255, Nº 1, 2014, págs. 106-121
• Idioma: inglés
• DOI: 10.1016/j.cam.2013.04.023
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• Resumen

  • 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.