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Name:

Miloslav Znojil

Reviewer number:

9689

Email:

znojil@ujf.cas.cz

Item's zbl-Number:

DE 018 728 672

Author(s):

Grammont, Laurence; Largillier, Alain:

Shorttitle:

On epsilon-spectra and stability radii

Source:

J. Comput. Appl. Math. 147, No. 2, 453 - 469

Classification:

65F15

Eigenvalues, eigenvectors

Primary Classification:

Secondary Classification:

Keywords:

epsilon-spectrum; Lyapunov stability; partitioning two by two; sufficient conditions of stability

Review:

Authors suggest that for large matrices A (one of illustrative
examples of which is 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.

Remarks to the editors:

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