Graduation Year
2021
Document Type
Open Access Senior Thesis
Degree Name
Bachelor of Science
Department
Mathematics
Reader 1
Jon Jacobsen
Reader 2
Jasper Weinburd
Terms of Use & License Information
Rights Information
2021 Eleanor Devin Byrnes
Abstract
Inspired by the fractals generated by the discretizations of the Continuous Newton Method and the notion of a fractional derivative, we ask what it would mean if such a fractional derivative were to replace the derivatives in Newton's Method. This work, largely experimental in nature, examines these new iterative methods by generating their Julia sets, computing their fractal dimension, and in certain tractable cases examining the behaviors using tools from dynamical systems.
Recommended Citation
Byrnes, Eleanor, "Fractals, Fractional Derivatives, and Newton-Like Methods" (2021). HMC Senior Theses. 244.
https://scholarship.claremont.edu/hmc_theses/244
Included in
Dynamic Systems Commons, Numerical Analysis and Computation Commons, Other Mathematics Commons
