Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Fourier extension based numerical integration scheme for fast and
  high-order approximation of convolutions with weakly singular kernels   Computationally efficient numerical methods for high-order approximations of
convolution integrals involving weakly singular kernels find many practical
applications including those in the development of fast quadrature methods for
numerical solution of integral equations. Most fast techniques in this
direction utilize uniform grid discretizations of the integral that facilitate
the use of FFT for $O(n\log n)$ computations on a grid of size $n$. In general,
however, the resulting error converges slowly with increasing $n$ when the
integrand does not have a smooth periodic extension. Such extensions, in fact,
are often discontinuous and, therefore, their approximations by truncated
Fourier series suffer from Gibb's oscillations. In this paper, we present and
analyze an $O(n\log n)$ scheme, based on a Fourier extension approach for
removing such unwanted oscillations, that not only converges with high-order
but is also relatively simple to implement. We include a theoretical error
analysis as well as a wide variety of numerical experiments to demonstrate its
efficacy.

19
The categories of this paper are: eess
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph