On the Superlinear Convergence of Newton’s Method on Riemannian Manifolds

Teles A. Fernandes (), Orizon P. Ferreira () and Jinyun Yuan ()
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Teles A. Fernandes: Universidade Estadual do Sudoeste da Bahia
Orizon P. Ferreira: Universidade Federal de Goiás
Jinyun Yuan: Universidade Federal do Paraná

Journal of Optimization Theory and Applications, 2017, vol. 173, issue 3, No 7, 828-843

Abstract: 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: Riemannian manifold; Newton’s method; Local convergence; Superlinear rate; 90C30; 49M15; 65K05 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10957-017-1107-2

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