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Brent Davis - PhD preliminary examination as follows:
Date: Thursday, December 22, 2016
Place: Weber 201
Time: 2:00 p.m.

Title:  Applications of Numerical Algebraic Geometry

Advisor:   Dr. Dan Bates    Co-Advisor:  Dr. Chris Peterson

Committee:   Dr. Michael Kirby,  Dr. Anthony Maciejewski

   Numerical algebraic geometry (NAG) is a collection of methods, based on homotopy continuation, to approximate solutions to polynomial systems of equations. NAG was largely motivated by problems in algebraic robot kinematics. In the last half-century, breakthroughs in the area have made it possible to solve large-scale polynomials that arise from science and engineering applications.

Fundamental ideas of NAG will first be discussed. Then, a new contribution to NAG call 'perturbed regeneration' will be presented. Perturbed regeneration is an efficient technique to find all isolated solutions to polynomials. Furthermore, a mathematical tool call the 'max length vector line of best fit' will be presented. The MLV line models a collection of data assumed to lie on a disjoint union of Grassmannian manifolds. The MLV line will be computed using NAG and then applied to a novel application using imaging date.