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    Avoiding singularities during homotopy continuation

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    http://hdl.handle.net/10217/181397
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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 ...
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    Author(s)
    Hodges, Timothy E.

    Advisor(s)
    Bates, Daniel J.

    Date Issued
    2017
    Format
    born digital; doctoral dissertations
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    • 2000-2019 - CSU Theses and Dissertations
    • Theses and Dissertations - Department of Mathematics

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