Article

Third-order methods on Riemannian manifolds under Kantorovich conditions This paper is dedicated to the memory of Sergio Plaza

Journal ar
Journal of Computational and Applied Mathematics
  • Volumen: 255
  • Fecha: 01 January 2014
  • Páginas: 106-121
  • ISSN: 03770427
  • Source Type: Journal
  • DOI: 10.1016/j.cam.2013.04.023
  • Document Type: Article
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. © 2013 Elsevier B.V. All rights reserved.

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