Open PhilippSchuette opened 1 year ago
As part of this issue it might also be worthwhile (in terms of efficiency) to consider a more dynamic refinement strategy: Depending on the currently estimated total number of roots the refinement procedure could choose to produce not two but maybe four or even something like 2 * #number of roots
rectangles.
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 / d
whered
is the distance to the nearest root off(z)
).