Numerical Integration for Composite Functions in Multidimensional Domains through a
Lebesgue Quadrature
Numerical integration; Quasi-Monte Carlo methods; Lebesgue quadratures
The present dissertation aims to introduce a numerical integration method, whose
application will run on domains containing a high number of dimensions. In this regard, the
developed methodology seeks to present a Lebesgue quadrature, which is based on partitions
of the image of a function, where each weight is associated with a value of the function
defined in its image. For Riemann-Integrable functions, we demonstrate the existence of a
Lebesgue quadrature and show how to construct quadratures of this type for composite
functions, in which the method exhibited good efficiency, surpassing quasi-Monte Carlo
methods. The method involves arbitrarily approximating the value of a given finite sum using
information generated by a histogram, to demonstrate that the numerical integration of a
composite function, whose argument’s density has been previously determined, can be
evaluated very easily.