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Universal algorithms for computing spectra of periodic operators

Ben-Artzi, Jonathan, Marletta, Marco and Rosler, Frank 2022. Universal algorithms for computing spectra of periodic operators. Numerische Mathematik 150 , pp. 719-767. 10.1007/s00211-021-01265-w

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Abstract

Schr\"odinger operators with periodic (possibly complex-valued) potentials and discrete periodic operators (possibly with complex-valued entries) are considered, and in both cases the computational spectral problem is investigated: namely, under what conditions can a `one-size-fits-all' algorithm for computing their spectra be devised? It is shown that for periodic banded matrices this can be done, as well as for Schr\"odinger operators with periodic potentials that are sufficiently smooth. In both cases implementable algorithms are provided, along with examples. For certain Schr\"odinger operators whose potentials may diverge at a single point (but are otherwise well-behaved) it is shown that there does not exist such an algorithm, though it is shown that the computation is possible if one allows for two successive limits.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Additional Information: This article is licensed under a Creative Commons Attribution 4.0 International License
Publisher: Springer
ISSN: 0029-599X
Funders: EPSRC, European Council
Date of First Compliant Deposit: 15 December 2021
Date of Acceptance: 10 December 2021
Last Modified: 30 Apr 2022 15:30
URI: https://orca.cardiff.ac.uk/id/eprint/146158

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