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.
Abstract template for Poznan Reasoning Week 2016. The template uses uses llncs class provided by Springer.
Poznań Reasoning Week, consisting of three conferences, aims at bringing together experts from various fields, whose research focus on reasoning processes and their modelling from three perspectives:
the interplay of logic and cognition (Logic and Cognition 2016);
formal modelling of reasoning and argumentation (14th ArgDiap);
natural question processing (QuestPro 2016).
The Legrand Orange Book LaTeX Template
Version 2.1.1 (14/2/16)
This template has been downloaded from:
Mathias Legrand (firstname.lastname@example.org) with modifications by:
CC BY-NC-SA 3.0
Chapter heading images should have a 2:1 width:height ratio,
e.g. 920px width and 460px height.