Utilize este identificador para referenciar este registo:
https://hdl.handle.net/1822/8803
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Campo DC | Valor | Idioma |
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dc.contributor.author | Ralha, Rui | - |
dc.date.accessioned | 2009-03-17T17:07:12Z | - |
dc.date.available | 2009-03-17T17:07:12Z | - |
dc.date.issued | 2009-02 | - |
dc.identifier.citation | "SIAM Journal on Matrix Analysis and Applications." ISSN 0895-4798. 31:1 (Feb.2009) 75-91. | en |
dc.identifier.issn | 0895-4798 | en |
dc.identifier.uri | https://hdl.handle.net/1822/8803 | - |
dc.description.abstract | Let $T$ be a symmetric tridiagonal matrix with entries and eigenvalues of different magnitudes. For some $T$, small entrywise relative perturbations induce small errors in the eigenvalues, independently of the size of the entries of the matrix; this is certainly true when the perturbed matrix can be written as $\widetilde{T}=X^{T}TX$ with small $||X^{T}X-I||$. Even if it is not possible to express in this way the perturbations in every entry of $T$, much can be gained by doing so for as many as possible entries of larger magnitude. We propose a technique which consists of splitting multiplicative and additive perturbations to produce new error bounds which, for some matrices, are much sharper than the usual ones. Such bounds may be useful in the development of improved software for the tridiagonal eigenvalue problem, and we describe their role in the context of a mixed precision bisection-like procedure. Using the very same idea of splitting perturbations (multiplicative and additive), we show that when $T$ defines well its eigenvalues, the numerical values of the pivots in the usual decomposition $T-\lambda I=LDL^{T}$ may be used to compute approximations with high relative precision. | en |
dc.description.sponsorship | Fundação para a Ciência e Tecnologia (FCT) - POCI 2010 | por |
dc.language.iso | eng | en |
dc.publisher | Society for Industrial and Applied Mathematics (SIAM) | en |
dc.rights | openAccess | en |
dc.subject | Symmetric tridiagonal matrices | en |
dc.subject | Eigenvalues | en |
dc.subject | Perturbation theory | en |
dc.title | Perturbation splitting for more accurate eigenvalues | en |
dc.type | article | por |
dc.peerreviewed | yes | en |
dc.relation.publisherversion | http://www.siam.org/journals/simax/31-1/68704.html | en |
sdum.number | 1 | en |
sdum.pagination | 75-91 | en |
sdum.publicationstatus | published | en |
sdum.volume | 31 | en |
oaire.citationStartPage | 75 | por |
oaire.citationEndPage | 91 | por |
oaire.citationIssue | 1 | por |
oaire.citationVolume | 31 | por |
dc.identifier.doi | 10.1137/070687049 | por |
dc.subject.wos | Science & Technology | por |
sdum.journal | SIAM Journal on Matrix Analysis and Applications | por |
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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Splitting.pdf | 226,37 kB | Adobe PDF | Ver/Abrir |