Before revision:  The algorithm removes standard restrictions for path following FoV methods that generally cannot deal with decomposing matrices A due to possible eigencurve crossings of H\!K {\cal  _A(t).
After revision:  The algorithm removes standard restrictions for path following FoV methods that generally cannot deal with decomposing matrices A due to possible eigencurve crossings of H\!K {\cal F _A(t).