  Three aspects of applying homotopy continuation, which is commonly used to
solve parameterized systems of polynomial equations, are investigated. First,
for parameterized systems which are homogeneous, we investigate options for
performing computations on an adaptively chosen affine coordinate patch.
Second, for parameterized systems which are overdetermined, we investigate
options for adaptively selecting a well-constrained subsystem to restore
numerical stability. Finally, since one is typically interested in only
computing real solutions for parameterized problems which arise from
applications, we investigate a scheme for heuristically identifying solution
paths which appear to be ending at nonreal solutions and truncating them. We
demonstrate these three aspects on two problems arising in computer vision.
