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.