Graduation Year

2005

Document Type

Open Access Senior Thesis

Degree Name

Bachelor of Science

Department

Mathematics

Reader 1

Jon T. Jacobsen

Reader 2

Lesley Ward

Abstract

There are many iterative techniques to find a root or zero of a given function. For any iterative technique, it is often of interest to know which initial seeds lead to which roots. When the iterative technique used is Newton’s Method, this is known as Cayley’s Problem. In this thesis, I investigate two extensions of Cayley’s Problem. In particular, I study generalizations of Newton’s Method, in both C and R2, and the associated fractal structures that arise from using more sophisticated numerical approximation techniques.

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