rparini
Literature Notes
Improving derivative-free case
When df is not provided we currently approximate it using a finite difference method
https://github.com/rparini/cxroots/blob/1b0c859736f301d61c85ca2e31d3c8c5b6406157/cxroots/root_counting.py#L197-L204
Is there a better way of doing this? I feel like knowing f is complex analytic should let us do something more clever but not sure what. I've seen literature involving contour integrations to do this (and I implemented an approach in the cxroots.derivative.cx_derivative function) but integration can involve a lot of function evaluations. Possibly relevant reading:
- Numerical Differentiation of Analytic Functions, Fornberg 1981
Alternatively, perhaps we could take a different approach to rootfinding that avoids approximating df when it is not provided. Possibly relevant reading:
- Computing zeros of analytic functions in the complex plane without using derivatives, 2006
- A Derivative-Free Algorithm for Computing Zeros of Analytic Functions
- A Numerical Method for Locating the Zeros of an Analytic Function suggests evaluating ln(f(z))
Cluster handling
Can we improve how we handle clusters of roots?
