Banca de DEFESA: LUCAS MATHEUS AUGUSTO OLIMPIO GUANABARA

Uma banca de DEFESA de MESTRADO foi cadastrada pelo programa.
STUDENT : LUCAS MATHEUS AUGUSTO OLIMPIO GUANABARA
DATE: 12/03/2024
TIME: 14:00
LOCAL: Ambiente virtual (https://meet.google.com/unw-qugk-ggp)
TITLE:

Numerical Integration for Composite Functions in Multidimensional Domains through a
Lebesgue Quadrature

KEY WORDS:

Numerical integration; Quasi-Monte Carlo methods; Lebesgue quadratures

PAGES: 69
BIG AREA: Ciências Exatas e da Terra
AREA: Probabilidade e Estatística
SUMMARY:

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.

COMMITTEE MEMBERS:
Externo à Instituição - GUARACI DE LIMA REQUENA - UFV
Interno - 3309089 - BRUNO DOS SANTOS SOLHEID
Interno - 3061368 - DIEGO FERRAZ DE SOUZA
Presidente - 3010614 - ELIARDO GUIMARAES DA COSTA