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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).
The text was updated successfully, but these errors were encountered:
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)
).The text was updated successfully, but these errors were encountered: