Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An O(N) Direct Solver for Integral Equations on the Plane   An efficient direct solver for volume integral equations with O(N) complexity
for a broad range of problems is presented. The solver relies on hierarchical
compression of the discretized integral operator, and exploits that
off-diagonal blocks of certain dense matrices have numerically low rank.
Technically, the solver is inspired by previously developed direct solvers for
integral equations based on "recursive skeletonization" and "Hierarchically
Semi-Separable" (HSS) matrices, but it improves on the asymptotic complexity of
existing solvers by incorporating an additional level of compression. The
resulting solver has optimal O(N) complexity for all stages of the computation,
as demonstrated by both theoretical analysis and numerical examples. The
computational examples further display good practical performance in terms of
both speed and memory usage. In particular, it is demonstrated that even
problems involving 10^{7} unknowns can be solved to precision 10^{-10} using a
simple Matlab implementation of the algorithm executed on a single core.

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The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: nlin
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat