Newton's method in Riemannian manifolds

Authors

  • Ioannis K. Argyros Cameron University, USA

Keywords:

Newton's method, Riemannian manifold, local/semilocal convergence, singularity of a vector field, Newton-Kantorovich method
Abstract views: 220

Abstract

Using more precise majorizing sequences than before [1], [8], and under the same computational cost, we provide a finer semilocal convergence analysis of Newton's method in Riemannian manifolds with the following advantages: larger convergence domain, finer error bounds on the distances involved, and a more precise information on the location of the singularity of the vector field.

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References

Alvarez, F., Bolte, J. and Munier, J., A unifying local convergence result for Newton's method in Riemannian manifolds, Institut National de Recherche en informatique et en automatique, Theme Num-Numeriques, Project, Sydoco, Rapport de recherche No. 5381, November 2004, France.

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Do Carano, M., Riemannian Geometry, Birkhäuser, Boston, 1992, https://doi.org/10.1007/978-1-4757-2201-7

Ferreira, O. P. and Svaiter, B. F., Kantorovich's theorem on Newton's method in Riemannian manifolds, J. Complexity, 18, pp. 304-353, 2002, https://doi.org/10.1006/jcom.2001.0582

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Published

2008-08-01

How to Cite

Argyros, I. K. (2008). Newton’s method in Riemannian manifolds. Rev. Anal. Numér. Théor. Approx., 37(2), 119–125. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/2008-vol37-no2-art3

Issue

Vol. 37 No. 2 (2008)

Section

Articles

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Copyright (c) 2015 Journal of Numerical Analysis and Approximation Theory

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