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View Full Version : Counting zeros of a complex function numerically


nick11
Jun6-11, 10:46 AM
Hi all,

I'm asking myself how to best numerically count the zeros of a, say, holomorphic function $\psi:\Omega\to\C$ where $\Omega$ is open and bounded in $\R^d$.

So far I only considered $d=2$ and just counted the phase jumps in $\arg\psi$ around the boundary of the domain, but that doesn't easily translate into $d=3$.
I've mostly been looking at Cauchy's integral theorem, the residual theorem and such so far.

Any ideas?