Abstract
This work presents a strategy of linesearch to find singularities of vector fields defined on Riemannian manifolds. It is an adapted of the Armijo rule for preventing a step length quite small on the Newton direction, when it exists. Otherwise, it is kept the Armijo rule in a safeguard direction. This strategy improves the damped Riemannian Newton method. Is given two exemple which the proposed algorithm can be apllied: to minimize a joint diagonalization problem on the Stiefel manifold, and to find singularities of a non-conservative vector field on the sphere.
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