Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Improve adjustment of search domains #35

Open
PhilippSchuette opened this issue Apr 29, 2023 · 1 comment
Open

Improve adjustment of search domains #35

PhilippSchuette opened this issue Apr 29, 2023 · 1 comment

Comments

@PhilippSchuette
Copy link
Member

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).
@PhilippSchuette
Copy link
Member Author

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.

Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment
Labels
None yet
Projects
None yet
Development

No branches or pull requests

1 participant