Finite sections: stability, spectral pollution and asymptotics of condition numbers and pseudospectra

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.

Schlagworte

Condition number

Pseudospectrum

Spectral pollution

Stability

DDC Class

510: Mathematics

Projekt(e)

Projekt DEAL

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https://creativecommons.org/licenses/by/4.0/

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1-s2.0-S0024379524002052-main.pdf

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main article

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625.38 KB

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Finite sections: stability, spectral pollution and asymptotics of condition numbers and pseudospectra