Adaptive strategies for solving parameterized systems using homotopy continuation

Dataset

Description

Three key aspects of applying homotopy continuation to parameterized systems of polynomial equations are investigated. First, for parameterized systems which are homogenized with solutions in projective space, we investigate options for selecting the affine patch where computations are performed. Second, for parameterized systems which are overdetermined, we investigate options for randomizing the system for improving the numerically stability of the computations. Finally, since one is typically interested in only computing real solutions for parameterized problems which arise from applications, we investigate a scheme for identifying solution paths which appear to be ending at nonreal solutions. We demonstrate these three aspects on minimal problems in computer vision.

Attributes

Attribute NameValues
Creator
  • Margaret Regan

  • Jonathan Hauenstein

Contributor
  • Sameer Agarwal

Publisher
  • Jonathan Hauenstein

Departments and Units
Access Rights Open Access
Content License
  • All rights reserved

Digital Object Identifier

doi:10.7274/R0C53HXK

This DOI is the best way to cite this dataset.

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