An Analysis of a Family of Root Finding Methods

Authors

• Arabella Fuzak, College of Saint Benedict and Saint John's University

Document Type

Thesis

Publication Date

4-30-2026

Disciplines

Mathematics

Advisor

Robert Hesse

Abstract

This thesis analyzes the behavior of a family of iterative root-finding methods, the Hansen-Patrick Family, which has a parameter, alpha, to create methods such as Newton’s methods, Halley’s method, and Euler’s method. By varying the parameter alpha, with both real and complex values, this project examines how the parameter can change convergence, divergence, and stability for different functions. This is shown by basin maps and Mandelbrot-like sets to visualize this behavior and classify points based on whether they converge to a root, diverge to infinity, or remain bounded without converging.

Recommended Citation

Fuzak, Arabella, "An Analysis of a Family of Root Finding Methods" (2026). Celebrating Scholarship and Creativity Day (2018-). 366.
https://digitalcommons.csbsju.edu/ur_cscday/366