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.