Utilize este identificador para referenciar este registo:
https://hdl.handle.net/1822/16203
Título: | Reliable eigenvalues of symmetric tridiagonals |
Autor(es): | Ralha, Rui |
Palavras-chave: | Symmetric tridiagonals Bisection method Bounds for eigenvalues |
Data: | Dez-2011 |
Editora: | Society for Industrial and Applied Mathematics |
Revista: | SIAM J Matrix Anal Appl. |
Resumo(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. |
Tipo: | Artigo |
URI: | https://hdl.handle.net/1822/16203 |
DOI: | 10.1137/100817413 |
ISSN: | 0895-4798 1095-7162 |
Versão da editora: | http://epubs.siam.org/sima/resource/1/sjmael/v32/i4/p1524_s1?isAuthorized=no |
Arbitragem científica: | yes |
Acesso: | Acesso aberto |
Aparece nas coleções: | CMAT - Artigos em revistas com arbitragem / Papers in peer review journals |
Ficheiros deste registo:
Ficheiro | Descrição | Tamanho | Formato | |
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reliable.pdf | Documento principal | 183,7 kB | Adobe PDF | Ver/Abrir |