Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the superlinear convergence of Newton's method on Riemannian
  manifolds   In this paper we study the Newton's method for finding a singularity of a
differentiable vector field defined on a Riemannian manifold. Under the
assumption of invertibility of covariant derivative of the vector field at its
singularity, we establish the well definition of the method in a suitable
neighborhood of this singularity. Moreover, we also show that the generated
sequence by Newton method converges for the solution with superlinear rate.

9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex