An algorithm for identifying eigenvectors exhibiting strong spatial localization

Ovall, Jeffrey; Reid, Robyn

doi:10.1090/mcom/3734

An algorithm for identifying eigenvectors exhibiting strong spatial localization
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by Jeffrey S. Ovall and Robyn Reid;

Math. Comp. 92 (2023), 1005-1031

DOI: https://doi.org/10.1090/mcom/3734

Published electronically: January 6, 2023

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Abstract:

We introduce an approach for exploring eigenvector localization phenomena for a class of (unbounded) selfadjoint operators. More specifically, given a target region and a tolerance, the algorithm identifies candidate eigenpairs for which the eigenvector is expected to be localized in the target region to within that tolerance. Theoretical results, together with detailed numerical illustrations of them, are provided that support our algorithm. A partial realization of the algorithm is described and tested, providing a proof of concept for the approach.

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Mathematics of Computation

An algorithm for identifying eigenvectors exhibiting strong spatial localization
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Abstract: