Newton's method in Riemannian manifolds

Author:

Argyros Ioannis K.

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.

Publisher

Academia Romana Filiala Cluj

Subject

Applied Mathematics,Computational Mathematics,Numerical Analysis,Mathematics (miscellaneous)

Reference10 articles.

1. 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.

2. Argyros, I. K., An improved convergence analysis and applications for Newton-like methods in Banach space, Numer. Funct. Anal. Optim., 24, nos. 7-8, pp. 653-672, 2003, https://doi.org/10.1081/nfa-120026364

3. Argyros, I. K., A unifying local-semilocal convergence and applications for two-point Newton-like methods in Banach space, J. Math. Anal. Applic., 298, pp. 374-397, 2004, https://doi.org/10.1016/j.jmaa.2004.04.008

4. Argyros, I. K., On the Newton-Kantorovich method in Riemannian manifolds, Advances in Nonlinear Variational Inequalities, 8, no. 2, pp. 81-85, 2005.

5. Argyros, I. K., Computational theory of iterative methods, Series: Studies in Computational Mathematics, 15, Editors, C.K. Chui and L. Wuytack, Elsevier Publ. Co., 2007, New-York, USA.

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1. Enlarging the convergence ball of Newton's method on Lie groups;Journal of Numerical Analysis and Approximation Theory;2015-12-18

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