Ben-Artzi, Jonathan; Marletta, Marco; Rösler, Frank (2022). Universal algorithms for computing spectra of periodic operators. Numerische Mathematik, 150(3), pp. 719-767. Springer 10.1007/s00211-021-01265-w
|
Text
s00211-021-01265-w.pdf - Published Version Available under License Creative Commons: Attribution (CC-BY). Download (5MB) | Preview |
Schrödinger 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 Schrödinger operators with periodic potentials that are sufficiently smooth. In both cases implementable algorithms are provided, along with examples. For certain Schrödinger 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: |
Journal Article (Original Article) |
|---|---|
Division/Institute: |
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics |
UniBE Contributor: |
Rösler, Frank |
Subjects: |
500 Science > 510 Mathematics |
ISSN: |
0945-3245 |
Publisher: |
Springer |
Language: |
German |
Submitter: |
Zarif Ibragimov |
Date Deposited: |
15 Mar 2023 07:47 |
Last Modified: |
15 Mar 2023 23:28 |
Publisher DOI: |
10.1007/s00211-021-01265-w |
BORIS DOI: |
10.48350/180067 |
URI: |
https://boris.unibe.ch/id/eprint/180067 |
Actions (login required)
 |
Edit item |