The matrix is hermitian (see In in image below) converting to a dense matrix and solving yields an eigenvector $\phi$ (In) which satisfies the eigenvector equation (Out). In a possibly related problem, when Eigensystem executes without quitting the Kernel, it consistently returns vectors which are not eigenvectors.Īn example $1220\times1220$ matrix which can be obtained using Import (not Get) can be found here. However, the kernel seems to unexpectedly quit (a problem which I have not diagnosed) during execution of Eigensystem. I have a family of sparse Hermitian cyclic-banded matrices $M$, and I want to calculate the smallest (absolute value) eigenvalue for each of them.
I would like to know if there are any known options or pre-conditioning methods which fix this, and which are feasible for large sparse matrices.
Short synopsis: for a specific family of sparse matrices, the eigensolver seems to be unstable (kernel quitting) for certain examples, and when it works it seems to consistently return vectors which are not eigenvectors.
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