  In the present paper, in order to fnd a singularity of a vector field defined
on Riemannian manifolds, we present a new globalization strategy of Newton
method and establish its global convergence with superlinear rate. In
particular, this globalization generalizes for a general retraction the
existing damped Newton's method. The presented global convergence analysis does
not require any hypotesesis on singularity of the vector field. We applied the
proposed method to solve the truncated singular value problem on the product of
two Stiefel manifolds, the dextrous hand grasping problem on the cone of
symmetric positive definite matrices and the Rayleigh quotient on the sphere.
Moreover, some academic problems are solved. Numerical experiments are
presented showing that the proposed algorithm has better robustness compared
with the aforementioned method.
