Degree Name

Master of Arts (MA)

Semester of Degree Completion

Fall 2019

Thesis Director

Bogdan V. Petrenko

Thesis Committee Member

Charles I. Delman

Thesis Committee Member

Andrew Parrish

Abstract

We will explore various numeric methods of finding roots of an analytic function over some open set of the complex plane. We will discuss a method of visually observing the roots, a gradient descent method for finding the roots of an analytic function, a gradient descent method for solving systems of analytic functions, and finally a method of descent that uses osculating circles to find roots of an analytic function. Of particular interest to this thesis are roots of complex polynomials. There will be examples, code snippets, and outputs of programs to illustrate all of these methods.

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