Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A fast direct solver for structured linear systems by recursive
  skeletonization   We present a fast direct solver for structured linear systems based on
multilevel matrix compression. Using the recently developed interpolative
decomposition of a low-rank matrix in a recursive manner, we embed an
approximation of the original matrix into a larger, but highly structured
sparse one that allows fast factorization and application of the inverse. The
algorithm extends the Martinsson/Rokhlin method developed for 2D boundary
integral equations and proceeds in two phases: a precomputation phase,
consisting of matrix compression and factorization, followed by a solution
phase to apply the matrix inverse. For boundary integral equations which are
not too oscillatory, e.g., based on the Green's functions for the Laplace or
low-frequency Helmholtz equations, both phases typically have complexity O(N)
in two dimensions, where $N$ is the number of discretization points. In our
current implementation, the corresponding costs in three dimensions are
$O(N^{3/2})$ and $O(N \log N)$ for precomputation and solution, respectively.
Extensive numerical experiments show a speedup of $\sim 100$ for the solution
phase over modern fast multipole methods; however, the cost of precomputation
remains high. Thus, the solver is particularly suited to problems where large
numbers of iterations would be required. Such is the case with ill-conditioned
linear systems or when the same system is to be solved with multiple right-hand
sides. Our algorithm is implemented in Fortran and freely available.

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The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: cs
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an