Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Unified Framework for Oscillatory Integral Transform: When to use
  NUFFT or Butterfly Factorization?   This paper concerns the fast evaluation of the matvec $g=Kf$ for $K\in
\mathbb{C}^{N\times N}$, which is the discretization of the oscillatory
integral transform $g(x) = \int K(x,\xi) f(\xi)d\xi$ with a kernel function
$K(x,\xi)=\alpha(x,\xi)e^{2\pi\i \Phi(x,\xi)}$, where $\alpha(x,\xi)$ is a
smooth amplitude function, and $\Phi(x,\xi)$ is a piecewise smooth phase
function with $O(1)$ discontinuous points in $x$ and $\xi$. A unified framework
is proposed to compute $Kf$ with $O(N\log N)$ time and memory complexity via
the non-uniform fast Fourier transform (NUFFT) or the butterfly factorization
(BF), together with an $O(N)$ fast algorithm to determine whether NUFFT or BF
is more suitable. This framework works for two cases: 1) explicit formulas for
the amplitude and phase functions are known, 2) only indirect access of the
amplitude and phase functions are available. Especially in the case of indirect
access, our main contributions are: 1) an $O(N\log N)$ algorithm for recovering
the amplitude and phase functions is proposed based on a new low-rank matrix
recovery algorithm, 2) a new stable and nearly optimal BF with amplitude and
phase functions in a form of a low-rank factorization (IBF-MAT) is proposed to
evaluate the matvec $Kf$. Numerical results are provided to demonstrate the
effectiveness of the proposed framework.

8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg