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Nonnormality estimation in projection‐type system realization methods
Author(s) -
Bazán F. S. V.
Publication year - 2008
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.598
Subject(s) - mathematics , realization (probability) , projection (relational algebra) , eigenvalues and eigenvectors , sensitivity (control systems) , matrix (chemical analysis) , type (biology) , normality , algorithm , basis (linear algebra) , statistics , geometry , ecology , physics , materials science , quantum mechanics , electronic engineering , engineering , composite material , biology
Using Henrici's departure from normality as a tool, we investigate the influence of nonnormality on the spectral sensitivity of system matrices of projection‐type system realization methods. Basically, we show that the system matrix of one of these methods is diagonally similar to the system matrix of the classical Kung's method and, we then conclude that the spectral sensitivity of all methods decreases significantly under conditions that are often met or easy to impose in practice. On the basis of these results, we conclude that all projection‐type realization methods have essentially the same spectral properties as Kung's method. Furthermore, a theoretical eigenvalue error bound is derived and illustrated by numerical simulations. Copyright © 2008 John Wiley & Sons, Ltd.