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.
Recommended Citation
Lewis, Owen, "Generalized Julia Sets: An Extension of Cayley's Problem" (2005). HMC Senior Theses. 172.
https://scholarship.claremont.edu/hmc_theses/172
Thesis Proposal
Owen Lewis.jpg (6 kB)
Picture of Owen Lewis
compEuler1_0.jpg (29 kB)
