Is there an algorithm (cheaper than solving the whole eigenspectrum) that determines the eigenvalue(s) of a (non-hermitian) matrix with the largest (magnitude of) complex component?
I have not found any online. Though, I saw a few nice algos that can determine the eigenvalues with largest magnitude.
Physical background of this problem is shown in arxiv 2003.03039:
More generally, is there an algo that can solve the eigenvalue with largest component on an arbitrary direction on the complex plane?
Any discussion is welcomed; maybe this is achievable on some particular matrices? Thanks in advance.