Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Infeasibility and error bound imply finite convergence of alternating
  projections   This paper combines two ingredients in order to get a rather surprising
result on one of the most studied, elegant and powerful tools for solving
convex feasibility problems, the method of alternating projections (MAP). Going
back to names such as Kaczmarz and von Neumann, MAP has the ability to track a
pair of points realizing minimum distance between two given closed convex sets.
Unfortunately, MAP may suffer from arbitrarily slow convergence, and sublinear
rates are essentially only surpassed in the presence of some Lipschitzian error
bound, which is our first ingredient. The second one is a seemingly unfavorable
and unexpected condition, namely, infeasibility. For two non-intersecting
closed convex sets satisfying an error bound, we establish finite convergence
of MAP. In particular, MAP converges in finitely many steps when applied to a
polyhedron and a hyperplane in the case in which they have empty intersection.
Moreover, the farther the target sets lie from each other, the fewer are the
iterations needed by MAP for finding a best approximation pair. Insightful
examples and further theoretical and algorithmic discussions accompany our
results, including the investigation of finite termination of other projection
methods.

5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
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The categories of this paper are: supr-con
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The categories of this paper are: eess
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph