Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Lebesgue Integral Quadrature   A new type of quadrature is developed. The Gaussian quadrature, for a given
measure, finds optimal values of a function's argument (nodes) and the
corresponding weights. In contrast, the Lebesgue quadrature developed in this
paper, finds optimal values of function (value-nodes) and the corresponding
weights. The Gaussian quadrature groups sums by function argument; it can be
viewed as a $n$-point discrete measure, producing the Riemann integral. The
Lebesgue quadrature groups sums by function value; it can be viewed as a
$n$-point discrete distribution, producing the Lebesgue integral.
Mathematically, the problem is reduced to a generalized eigenvalue problem:
Lebesgue quadrature value-nodes are the eigenvalues and the corresponding
weights are the square of the averaged eigenvectors. A numerical estimation of
an integral as the Lebesgue integral is especially advantageous when analyzing
irregular and stochastic processes. The approach separates the outcome
(value-nodes) and the probability of the outcome (weight). For this reason, it
is especially well-suited for the study of non-Gaussian processes. The software
implementing the theory is available from the authors.

12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas