Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the equivalence of the Hermitian eigenvalue problem and hypergraph
  edge elimination   It is customary to identify sparse matrices with the corresponding adjacency
or incidence graph. For the solution of linear systems of equations using
Gaussian elimination, the representation by its adjacency graph allows a
symbolic computation that can be used to predict memory footprints and enables
the determination of near-optimal elimination orderings based on heuristics.
The Hermitian eigenvalue problem on the other hand seems to evade such
treatment at first glance due to its inherent iterative nature. In this paper
we prove this assertion wrong by showing the equivalence of the Hermitian
eigenvalue problem with a symbolic edge elimination procedure. A symbolic
calculation based on the incidence graph of the matrix can be used in analogy
to the symbolic phase of Gaussian elimination to develop heuristics which
reduce memory footprint and computations. Yet, we also show that the question
of an optimal elimination strategy remains NP-hard, in analogy to the linear
systems case.

17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
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The categories of this paper are: eess
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: stat
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat