Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fast Algorithms for the computation of Fourier Extensions of arbitrary
  length   Fourier series of smooth, non-periodic functions on $[-1,1]$ are known to
exhibit the Gibbs phenomenon, and exhibit overall slow convergence. One way of
overcoming these problems is by using a Fourier series on a larger domain, say
$[-T,T]$ with $T>1$, a technique called Fourier extension or Fourier
continuation. When constructed as the discrete least squares minimizer in
equidistant points, the Fourier extension has been shown shown to converge
geometrically in the truncation parameter $N$. A fast ${\mathcal O}(N \log^2
N)$ algorithm has been described to compute Fourier extensions for the case
where $T=2$, compared to ${\mathcal O}(N^3)$ for solving the dense discrete
least squares problem. We present two ${\mathcal O}(N\log^2 N )$ algorithms for
the computation of these approximations for the case of general $T$, made
possible by exploiting the connection between Fourier extensions and Prolate
Spheroidal Wave theory. The first algorithm is based on the explicit
computation of so-called periodic discrete prolate spheroidal sequences, while
the second algorithm is purely algebraic and only implicitly based on the
theory.

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The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th