Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A diffusion-map-based algorithm for gradient computation on manifolds
  and applications   We recover the Riemannian gradient of a given function defined on interior
points of a Riemannian submanifold in the Euclidean space based on a sample of
function evaluations at points in the submanifold. This approach is based on
the estimates of the Laplace-Beltrami operator proposed in the diffusion-maps
theory. The Riemannian gradient estimates do not involve differential terms.
Analytical convergence results of the Riemannian gradient expansion are proved.
We apply the Riemannian gradient estimate in a gradient-based algorithm
providing a derivative-free optimization method. We test and validate several
applications, including tomographic reconstruction from an unknown random angle
distribution, and the sphere packing problem in dimensions 2 and 3.

16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
2
The categories of this paper are: math
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg