Iterative eigensolvers such as ARPACK, give the option to find a subset of the eigenvalues which have the largest imaginary part. My question is how do these algorithms work.

As I understand it, generally such algorithms use Krylov spaces and shift-invert methods which are very good at finding eigenvalues either at the extremes of the spectrum or around a given value. This is essentially because repeated applications of a matrix projects onto the eigenvector with largest magnitude eigenvalue. However, since the imaginary part of an eigenvalue need not have any correlation with its real part, I can't see how it's able to `ignore' the real part.

If anyone has any idea how these algorithms work, or alternatively a way to search for eigenvalues which is ignorant of the real part of the eigenvalue I'd be very grateful.

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    $\begingroup$ You may have more luck here using the numerical-methods tag instead of the computer-science tag. I found it purely by coincidence via scicomp $\endgroup$ – Carl Christian Dec 13 '17 at 23:01

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