Currently we implement the most basic adjustment strategy imaginable for search (sub-)rectangles: If a root falls exactly on the rectangle boundary then the boundary gets adjusted. This should be improved as follows:
- Rectangle boundaries should already be adjusted if
f'(z) / f(z) becomes too small (substitution in the argument principle integral shows that f'(z) / f(z) ~ 1 / d where d is the distance to the nearest root of f(z)).
- The strategy regarding how that particular boundary segment gets adjusted should be improved (the resulting rectangle should reliably be larger, not smaller).
Currently we implement the most basic adjustment strategy imaginable for search (sub-)rectangles: If a root falls exactly on the rectangle boundary then the boundary gets adjusted. This should be improved as follows:
f'(z) / f(z)becomes too small (substitution in the argument principle integral shows thatf'(z) / f(z) ~ 1 / dwheredis the distance to the nearest root off(z)).