On \(\varepsilon\)-spectra and stability radii
The authors suggest that for large matrices \(A\) (one of illustrative examples of which is the Wilkinson matrix), the analysis of the epsilon spectra (= sets where the resolvent is large) should be done, in parallel, also for certain diagonal submatrices of \(A\). Within this framework they analyse the simplest case (of a two-by-two partitioning) and study its details (new upper bound for the resolvent and its consequences, the influence of the off-diagonal components, a lower bound for a stability radius etc). Consequences are discussed for the Lyapunov stability (illustration: Orr-Sommerfeld operator) and for the reliability of the Krylov-subspace iteration techniques.
scientific article; zbMATH DE number 1872867