Hodges, Timothy E., authorBates, Daniel J., advisorBöhm, A. P., committee memberHulpke, Alexander, committee memberPeterson, Christopher, committee member2017-06-092017-06-092017http://hdl.handle.net/10217/181397In numerical algebraic geometry, the goal is to find solutions to a polynomial system F(x1,x2,...xn). This is done through a process called homotopy continuation. During this process, it is possible to encounter areas of ill-conditioning. These areas can cause failure of homotopy continuation or an increase in run time. In this thesis, we formalize where these areas of ill-conditioning can happen, and give a novel method for avoiding them. In addition, future work and possible improvements to the method are proposed. We also report on related developments in the Bertini software package. In addition, we discuss new infrastructure and heuristics for tuning configurations during homotopy continuation.born digitaldoctoral dissertationsengCopyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.branch pointsnumerical algebraic geometrysoftware developmenthomotopy continuationBertiniramification pointsText