An algorithm for identifying eigenvectors exhibiting strong spatial localization

An algorithm for identifying eigenvectors exhibiting strong spatial localization
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DOI：
10.1090/mcom/3734
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发表时间：
2021-05
期刊：
ArXiv
影响因子：
--
通讯作者：
Jeffrey S. Ovall;Robyn Reid
Jeffrey S. Ovall;Robyn Reid
中科院分区：
其他
文献类型：
--
作者：
Jeffrey S. Ovall;Robyn Reid

文献摘要

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我们介绍了一种方法来探索特征向量局部化现象的一类（无界）自伴算子。更具体地，给定目标区域和容限，该算法识别候选本征对，对于该候选本征对，期望本征向量在该容限内定位在目标区域中。理论结果，连同它们的详细数值说明，提供支持我们的算法。该算法的部分实现的描述和测试，提供了一个概念证明的方法。
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.