Please use this identifier to cite or link to this item:

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.
Publisher version
AccessOpen access
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

Files in This Item:
File Description SizeFormat 
reliable.pdfDocumento principal183,7 kBAdobe PDFView/Open

Partilhe no FacebookPartilhe no TwitterPartilhe no DeliciousPartilhe no LinkedInPartilhe no DiggAdicionar ao Google BookmarksPartilhe no MySpacePartilhe no Orkut
Exporte no formato BibTex mendeley Exporte no formato Endnote Adicione ao seu ORCID