# Damped Newton's Method on Riemannian Manifolds

arXiv: https://arxiv.org/abs/1803.05126 · HTML: https://mlsanity.com/paper/1803.05126/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Mar 2018.

## Built on by (most cited first, 1 of 1)

- [A diffusion-map-based algorithm for gradient computation on manifolds and applications](https://mlsanity.com/paper/2108.06988/) (2021)

## Abstract (arXiv)

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.