Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The rate of linear convergence of the Douglas-Rachford algorithm for
  subspaces is the cosine of the Friedrichs angle   The Douglas-Rachford splitting algorithm is a classical optimization method
that has found many applications. When specialized to two normal cone
operators, it yields an algorithm for finding a point in the intersection of
two convex sets. This method for solving feasibility problems has attracted a
lot of attention due to its good performance even in nonconvex settings.
  In this paper, we consider the Douglas-Rachford algorithm for finding a point
in the intersection of two subspaces. We prove that the method converges
strongly to the projection of the starting point onto the intersection.
Moreover, if the sum of the two subspaces is closed, then the convergence is
linear with the rate being the cosine of the Friedrichs angle between the
subspaces. Our results improve upon existing results in three ways: First, we
identify the location of the limit and thus reveal the method as a best
approximation algorithm; second, we quantify the rate of convergence, and
third, we carry out our analysis in general (possibly infinite-dimensional)
Hilbert space. We also provide various examples as well as a comparison with
the classical method of alternating projections.

15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
18
The categories of this paper are: econ
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex