Repeated iteration of a Collatz-type function

• Main Authors: Navarro, Louelle Dawn P., Olviga, Mari Nelle O.
• Format: text
• Language: English
• Published: Animo Repository 1998
• Subjects: Functions; Algorithms; Numerical analysis; Iterative methods (Mathematics)
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/16506
• Institution: De La Salle University

This study provides detailed exposition of Collatz 3X + 1 problem which concerns the behavior of the iterates of the function which takes odd integer n to 3n+1/2 and even integer to n/2. The main result contained in the article by Daniel A. Rawsthorne entitled Imitation of an Iteration gives a probabilistic approach to the question whether repeated iteration of a Collatz-type function always converges to 1. It is the proof of this main result that is discussed in this paper in great detailed. The researchers introduced some definitions with given examples which are necessary to understand the concept discussed in the article. The proof of the main result was expanded and presented in a comprehensible manner.