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Approximated structured pseudospectra
Author(s) -
Noschese Silvia,
Reichel Lothar
Publication year - 2017
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.2082
Subject(s) - rank (graph theory) , eigenvalues and eigenvectors , mathematics , computation , sensitivity (control systems) , matrix (chemical analysis) , mathematical optimization , algorithm , combinatorics , physics , materials science , quantum mechanics , electronic engineering , engineering , composite material
Summary Pseudospectra and structured pseudospectra are important tools for the analysis of matrices. Their computation, however, can be very demanding for all but small matrices. A new approach to compute approximations of pseudospectra and structured pseudospectra, based on determining the spectra of many suitably chosen rank‐one or projected rank‐one perturbations of the given matrix is proposed. The choice of rank‐one or projected rank‐one perturbations is inspired by Wilkinson's analysis of eigenvalue sensitivity. Numerical examples illustrate that the proposed approach gives much better insight into the pseudospectra and structured pseudospectra than random or structured random rank‐one perturbations with lower computational burden. The latter approach is presently commonly used for the determination of structured pseudospectra.