Integração numérica para funções compostas em domínios multidimensionais através de uma quadratura de Lebesgue

Abstract

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.