Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Computing the Riemannian logarithm on the Stiefel manifold: metrics,
  methods and performance   We address the problem of computing Riemannian normal coordinates on the
real, compact Stiefel manifold of orthogonal frames. The Riemannian normal
coordinates are based on the so-called Riemannian exponential and the
Riemannian logarithm maps and enable to transfer almost any computational
procedure to the realm of the Stiefel manifold. To compute the Riemannian
logarithm is to solve the (local) geodesic endpoint problem. Instead of
restricting the consideration to geodesics with respect to a single selected
metric, we consider a family of Riemannian metrics introduced by H\"uper,
Markina and Silva-Leite that includes the Euclidean and the canonical metric as
prominent examples.
  As main contributions, we provide (1) a unified, structured, reduced formula
for the Stiefel geodesics for the complete family of metrics, (2) a unified
method to tackle the geodesic endpoint problem, (3) an improvement of the
existing Riemannian log map under the canonical metric. The findings are
illustrated by means of numerical examples, where the novel algorithms prove to
be the most efficient methods known to this date.

13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an