Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multidimensional Phase Recovery and Interpolative Decomposition
  Butterfly Factorization   This paper focuses on the fast evaluation of the matvec $g=Kf$ for $K\in
\mathbb{C}^{N\times N}$, which is the discretization of a multidimensional
oscillatory integral transform $g(x) = \int K(x,\xi) f(\xi)d\xi$ with a kernel
function $K(x,\xi)=e^{2\pi\i \Phi(x,\xi)}$, where $\Phi(x,\xi)$ is a piecewise
smooth phase function with $x$ and $\xi$ in $\mathbb{R}^d$ for $d=2$ or $3$. A
new framework is introduced to compute $Kf$ with $O(N\log N)$ time and memory
complexity in the case that only indirect access to the phase function $\Phi$
is available. This framework consists of two main steps: 1) an $O(N\log N)$
algorithm for recovering the multidimensional phase function $\Phi$ from
indirect access is proposed; 2) a multidimensional interpolative decomposition
butterfly factorization (MIDBF) is designed to evaluate the matvec $Kf$ with an
$O(N\log N)$ complexity once $\Phi$ is available. Numerical results are
provided to demonstrate the effectiveness of the proposed framework.

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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: q-bio
3
The categories of this paper are: physics
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The categories of this paper are: nlin