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Based on the paper Sometimes Newton's Method Cycles, we first asked ourselves if there were any Newtonian Method Cycle functions which have non-trivial guesses. We encountered a way to create functions that cycle between a set number of points with any initial, non-trivial guesses when Newton's Method is applied. We exercised these possibilities through the methods of 2-cycles, 3-cycles and 4-cycles. We then generalized these cycles into k-cycles. After generalizing Newton's Method, we found the conditions that skew the cycles into a spiral pattern which will either converge, diverge or become a near-cycle. Once we obtained all this information, we explored additional questions that rose up from our initial exploration of Newton's Method.
Template for NAPPN annual meeting proceedings.
A minor modification of the SPIE proceedings template https://www.overleaf.com/latex/templates/spie-proceedings-style-template-and-guidelines-for-authors/qpkhfttzvnhz for the
Modificação do template de Rodrigo Cavalcante (https://www.overleaf.com/articles/plano-de-aula/chhjxtdqjsqk) onde separei o main.tex em vários arquivos para melhor localização dos tópicos e coloquei alguns pacotes para auxiliar na escrita e na bibliografia (biblatex-abnt). Adicionei também uma tabela para especificar a programação semestral caso o template seja utilizado como Plano de Ensino.
Geraldo Pereira
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