Adaptive strategies for solving parameterized systems using homotopy continuation



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.


Attribute NameValues
  • Margaret Regan

  • Jonathan Hauenstein

  • Sameer Agarwal

  • Jonathan Hauenstein

Departments and Units
Record Visibility Public
Content License
  • All rights reserved

Digital Object Identifier


This DOI is the best way to cite this dataset.


Please Note: You may encounter a delay before a download begins. Large or infrequently accessed files can take several minutes to retrieve from our archival storage system.