Damped Newton's Method on Riemannian Manifolds
Optimization and Control
2018-07-20 v2
Abstract
A damped Newton's method to find a singularity of a vector field in Riemannian setting is presented with global convergence study. It is ensured that the sequence generated by the proposed method reduces to a sequence generated by the Riemannian version of the classical Newton's method after a finite number of iterations, consequently its convergence rate is superlinear/quadratic. Moreover, numerical experiments illustrate that the damped Newton's method has better performance than Newton's method in number of iteration and computational time.
Keywords
Cite
@article{arxiv.1803.05126,
title = {Damped Newton's Method on Riemannian Manifolds},
author = {M. A. A. Bortoloti and T. A. Fernandes and O. P. Ferreira and Jinyun Yuan},
journal= {arXiv preprint arXiv:1803.05126},
year = {2018}
}