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 for such A . Tests and numerical comparisons are included   .
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_A(t) . Tests and numerical comparisons are included .