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How to Deduce a Proper Eigenvalue Cluster from a Proper Singular Value Cluster in the Nonnormal Case.
- Source :
-
SIAM Journal on Matrix Analysis & Applications . 2005, Vol. 27 Issue 1, p82. 5p. - Publication Year :
- 2005
-
Abstract
- We consider a generic sequence of matrices (the nonnormal case is of interest) showing a proper cluster at zero in the sense of the singular values. By a direct use of the notion of majorizations, we show that the uniform spectral boundedness is sufficient for the proper clustering at zero of the eigenvalues: if the assumption of boundedness is removed, then we can construct sequences of matrices with a proper singular value clustering and having all the eigenvalues of an arbitrarily big modulus. Applications to the preconditioning theory are discussed. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 08954798
- Volume :
- 27
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- SIAM Journal on Matrix Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 18245357
- Full Text :
- https://doi.org/10.1137/040608027