Secant Method on Riemannian Manifolds

TL;DR

This paper introduces a novel secant method adapted for complete Riemannian manifolds, leveraging differential geometry to find zeros of vector fields more generally than classical Euclidean approaches.

Contribution

It extends the classical secant method to Riemannian manifolds, providing a new numerical algorithm for zero-finding in a geometric context.

Findings

The method successfully generalizes secant method to Riemannian settings.

The algorithm converges under certain geometric conditions.

Potential applications in geometric analysis and optimization.

Abstract

In this work, by using techniques and results of differential geometry, we propose a new numerical method on complete Riemannian manifolds to find zeros of vector fields. Our algorithm generalizes the classical secant method