Homotopy methods [123,459,219] are
mathematically elegant, but unfortunately, investigation of such
methods indicates that they tend to be numerically ill-conditioned.
If
we try to get around this problem by implementing the algorithm in
rational arithmetic, we end up with enormous memory requirements
because we have to solve large systems of complex initial value
problems (IVP).
Interval methods can be applied to the solution of these IVPs but they
can be slow in practice [259].
