Dissertation/Thesis Abstract

Gale duality, decoupling, parameter homotopies, and monodromy
by Niemerg, Matthew E., Ph.D., Colorado State University, 2014, 116; 3624318
Abstract (Summary)

Numerical Algebraic Geometry (NAG) has recently seen significantly increased application among scientists and mathematicians as a tool that can be used to solve nonlinear systems of equations, particularly polynomial systems. With the many recent advances in the field, we can now routinely solve problems that could not have been solved even 10 years ago. We will give an introduction and overview of numerical algebraic geometry and homotopy continuation methods; discuss heuristics for preconditioning fewnomial systems, as well as provide a hybrid symbolic-numerical algorithm for computing the solutions of these types of polynomials and associated software called galeDuality; describe a software module of bertini named paramotopy that is scientific software specifically designed for large-scale parameter homotopy runs; give two examples that are parametric polynomial systems on which the aforementioned software is used; and finally describe two novel algorithms, decoupling and a heuristic that makes use of monodromy.

Indexing (document details)
Advisor: Bates, Daniel J.
Commitee: Lee, Chihoon, Peterson, Christopher, Shipman, Patrick
School: Colorado State University
Department: Mathematics
School Location: United States -- Colorado
Source: DAI-B 75/10(E), Dissertation Abstracts International
Subjects: Mathematics
Keywords: Gale duality, Monodromy, Numerical algebraic geometry, Parameter homotopies
Publication Number: 3624318
ISBN: 978-1-303-97572-1
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