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In this paper, we study Newton’s method for finding a singularity of a differentiable vector field defined on a Riemannian manifold. Under the assumption of invertibility of the covariant derivative… Click to show full abstract
In this paper, we study Newton’s method for finding a singularity of a differentiable vector field defined on a Riemannian manifold. Under the assumption of invertibility of the covariant derivative of the vector field at its singularity, we show that Newton’s method is well defined in a suitable neighborhood of this singularity. Moreover, we show that the sequence generated by Newton’s method converges to the solution with superlinear rate.
Keywords:
convergence newton;
superlinear convergence;
method;
method riemannian;
riemannian manifolds;
newton method
Journal Title: Journal of Optimization Theory and Applications
Year Published: 2017
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Journal Title: Journal of Optimization Theory and Applications
Year Published: 2017
Link to full text (if available)
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recommendations!