Date of Award
8-2025
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
School of Mathematical and Statistical Sciences
Committee Chair/Advisor
Michael Burr
Committee Member
James Coykendall
Committee Member
Brian Dean
Committee Member
Shuhong Gao
Committee Member
Svetlana Poznanovikj
Abstract
One of the fundamental problems in mathematics is to determine the set of solutions to a system of equations. In algebraic geometry, the equations studied are polynomials, and the solution set is called an algebraic variety. For single variable polynomials of degree less than five, the roots can be determined exactly using algebraic methods, but for polynomials of degree five or higher, numerical methods are required. When using numerical methods, it is important to know when the computed approximation is indeed a correct solution, which leads to the idea of a certified algorithm. An algorithm is said to be certified if it outputs both the solution to the problem and a certificate (a proof) that the solution is correct. In this dissertation, I study the problem of approximating algebraic curves using certified methods with a focus on correctly handling intersection points of the curves.
Recommended Citation
Byrd, Michael Jr., "Certified Approximation Algorithms of Algebraic Curves" (2025). All Dissertations. 4083.
https://open.clemson.edu/all_dissertations/4083
Author ORCID Identifier
0009-0005-0998-0433