Lindner, MarkoMarkoLindnerSchmeckpeper, DennisDennisSchmeckpeper2024-07-092024-07-092024-09-15Linear Algebra and Its Applications 697: 583-614 (2024)https://hdl.handle.net/11420/48267The 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.en0024-37952024583614Elsevierhttps://creativecommons.org/licenses/by/4.0/Condition numberPseudospectrumSpectral pollutionStabilityNatural Sciences and Mathematics::510: MathematicsJournal Article10.15480/882.1313210.1016/j.laa.2024.05.00610.15480/882.13132Journal Article