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arXiv · 1803.05126

Damped Newton's Method on Riemannian Manifolds

M. A. A. Bortoloti·T. A. Fernandes·O. P. Ferreira·Jinyun Yuan
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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.

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M. A. A. Bortoloti, T. A. Fernandes, O. P. Ferreira, Jinyun Yuan. 2018-03-14. Damped Newton's Method on Riemannian Manifolds. https://arxiv.org/abs/1803.05126

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