O algoritmo PageRank: uma abordagem numérica para a classificação de páginas da web

• Main Author: Silva, Marcos Vinícius da
• Publication Date: 2023
• Format: Bachelor thesis
• Language: por
• Source: Repositório Institucional da UTFPR (da Universidade Tecnológica Federal do Paraná (RIUT))
• Download full: http://repositorio.utfpr.edu.br/jspui/handle/1/36507
• topic: Autovalores; Markov, Processos de; Python (Linguagem de programação de computador); Eigenvalues; Markov processes; Python (Computer program language); CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA

This work aims to study the concepts of linear algebra and numerical calculus behind of the search algorithm used by Google, PageRank. The algorithm uses a system of linear equations to describe the connections between the corresponding pages. In order to simplify the problem, we perform algebric manipulations to transform the matrix that represents such a system into a Markov Matrix, through such a matrix, the largest eigenvalue corresponding to the matrix that describes the system of equations and consequently the largest corresponding eigenvector, which will be the stochastic vector that presents the relevance of each site in the given search. For if dealing with a system of equations with numerous unknowns there is no analytical solution for the problem, because of that it is necessary a numerical approximation for the resolution, we use the power method implemented in Python to find the solution vector of the problem.