Aspectos teóricos e computacionais em polinômios

• Ano de defesa: 2019
• Autor(a) principal: Oliveira Junior, Evaldir Barbosa de
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Mato Grosso; Brasil; Instituto de Ciências Exatas e da Terra (ICET) – Araguaia; UFMT CUA - Araguaia; Programa de Pós-Graduação em Matemática - PROFMAT
• Palavras-chave em Português: Polinômios; Método de Newton-Raphson; Polinômios simétricos; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA; Polynomials; Newton-Raphson Method; Symmetric polynomials
• Link de acesso: http://ri.ufmt.br/handle/1/3135

In this work we study ways to find polynomial roots computationally and their algebraic properties. We use two excellent tools for that: the Newton-Raphson Method and the Symmetric Polynomials theory. In the first part, we demonstrate the local convergence of the Newton-Raphson Method for real functions. We also perform a study to verify the existence and location of the roots of a polynomial through the Descartes’ Rule of Signs and Sturm Sequences. In particular, we make a detailed study of the Newton- Raphson Method to find the nth root of a positive number. Next, we study symmetric polynomials: a very useful tool for solving algebraic problems of factorization, non-linear equation systems, linear recurrence equations and some algebraic equations. At the end, a list of solved exercises is presented, aiming at fixing these subjects.