Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quadrature rules for $C^0$ and $C^1$ splines, a recipe   Closed formulae for all Gaussian or optimal, 1-parameter quadrature rules in
a compact interval [a, b] with non uniform, asymmetric subintervals, arbitrary
number of nodes per subinterval for the spline classes $S_{2N, 0}$ and
$S_{2N+1, 1}$, i.e. even and odd degree are presented. Also rules for the 2
missing spline classes $S_{2N-1, 0}$ and $S_{2N, 1}$ (the so called 1/2-rules),
i.e. odd and even degree are presented. These quadrature rules are explicit in
the sense, that they compute the nodes and their weights in the first/last
boundary subinterval and, via a recursion the other nodes/weights, parsing from
the first/last subinterval to the middle of the interval. These closed formulae
are based on the semi-classical Jacobi type orthogonal polynomials.

23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
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: acc-phys
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph