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Finite sections: stability, spectral pollution and asymptotics of condition numbers and pseudospectra
Citation Link: https://doi.org/10.15480/882.13132
Publikationstyp
Journal Article
Date Issued
2024-09-15
Sprache
English
Author(s)
Schmeckpeper, Dennis
TORE-DOI
Volume
697
Start Page
583
End Page
614
Citation
Linear Algebra and Its Applications 697: 583-614 (2024)
Publisher DOI
Scopus ID
Publisher
Elsevier
The stability of an approximating sequence (An) for an operator A usually requires, besides invertibility of A, the invertibility of further operators, say B,C,…, that are well-associated to the sequence (An). We study this set, {A,B,C,…}, of so-called stability indicators of (An) and connect it to the asymptotics of ‖An‖, ‖An−1‖ and κ(An)=‖An‖‖An−1‖ as well as to spectral pollution by showing that limsupSpecεAn=SpecεA∪SpecεB∪SpecεC∪…. We further specify, for each of ‖An‖, ‖An−1‖, κ(An) and SpecεAn, under which conditions even convergence applies.
Subjects
Condition number
Pseudospectrum
Spectral pollution
Stability
DDC Class
510: Mathematics
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1-s2.0-S0024379524002052-main.pdf
Type
Main Article
Size
625.38 KB
Format
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