Damped Newton's Method on Riemannian Manifolds
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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