Please use this identifier to cite or link to this item: http://hdl.handle.net/1822/16203

TitleReliable eigenvalues of symmetric tridiagonals
Author(s)Ralha, Rui
KeywordsSymmetric tridiagonals
Bisection method
Bounds for eigenvalues
Issue dateDec-2011
PublisherSociety for Industrial and Applied Mathematics
JournalSIAM J Matrix Anal Appl.
Abstract(s)For the eigenvalues of a symmetric tridiagonal matrix T, the most accurate algorithms deliver approximations which are the exact eigenvalues of a matrix whose entries differ from the corresponding entries of T by small relative perturbations. However, for matrices with eigenvalues of different magnitudes, the number of correct digits in the computed approximations for eigenvalues of size smaller than ‖T‖₂ depends on how well such eigenvalues are defined by the data. Some classes of matrices are known to define their eigenvalues to high relative accuracy but, in general, there is no simple way to estimate well the number of correct digits in the approximations. To remedy this, we propose a method that provides sharp bounds for the eigenvalues of T. We present some numerical examples to illustrate the usefulness of our method.
TypeArticle
URIhttp://hdl.handle.net/1822/16203
DOI10.1137/100817413
ISSN0895-4798
1095-7162
Publisher versionhttp://epubs.siam.org/sima/resource/1/sjmael/v32/i4/p1524_s1?isAuthorized=no
Peer-Reviewedyes
AccessOpen access
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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