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### Time and memory required to diagonalize a 18000 by 18000 matrix using numpy in python

A 20000 by 20000 double-precision complex matrix requires $20000 \times 20000 \times 8 \times 2=6.4 \mbox{gigabytes}$ of RAM. The LAPACK routines ZHEEV that will do the work for you will store the ...
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### Quality of eigenvalue approximation in Lanczos method

The convergence behavior you are seeing is actually expected. One of things that makes the Lanczos method so interesting is that it does a good job of simultaneously converging eigenvalues at both ...
• 6,074
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### Generalization of eigendecomposition problem

Yes. You could rewrite it as $$B v = \lambda v\,$$ with $B = A - M$, $M = \textrm{diag}(\mu)$.
• 8,515
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### Correct eigenfunctions of Laplace operator by Finite Differences

You should specify the eigenvalues you want with which="SM", for example. Check the following snippet. I also changed the solver, since your system is symmetric. <...
• 8,515
Accepted

### Eigenvector with maximum overlap

The following paper suggests that the Jacobi-Davidson method can be used to target eigenvectors based on "any property that can be computed from the eigenvector", which would seem to include overlap ...
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