Avoiding singularities during homotopy continuation
Date
2017
Authors
Hodges, Timothy E., author
Bates, Daniel J., advisor
Böhm, A. P., committee member
Hulpke, Alexander, committee member
Peterson, Christopher, committee member
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Abstract
In 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.
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Subject
branch points
numerical algebraic geometry
software development
homotopy continuation
Bertini
ramification points