Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rapid Application of the Spherical Harmonic Transform via Interpolative
  Decomposition Butterfly Factorization   We describe an algorithm for the application of the forward and inverse
spherical harmonic transforms. It is based on a new method for rapidly
computing the forward and inverse associated Legendre transforms by
hierarchically applying the interpolative decomposition butterfly factorization
(IDBF). Experimental evidence suggests that the total running time of our
method -- including all necessary precomputations -- is $\mathcal{O}(N^2
\log^3(N))$, where $N$ is the order of the transform. This is nearly
asymptotically optimal. Moreover, unlike existing algorithms which are
asymptotically optimal or nearly so, the constant in the running time of our
algorithm is small enough to make it competitive with state-of-the-art
$\mathcal{O}\left(N^3\right)$ methods at relatively small values of $N$.
Numerical results are provided to demonstrate the effectiveness and numerical
stability of the new framework.

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The categories of this paper are: physics
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: dg-ga
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: nlin
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The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
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The categories of this paper are: supr-con