Matches in SemOpenAlex for { <https://semopenalex.org/work/W2287275630> ?p ?o ?g. }
Showing items 1 to 71 of
71
with 100 items per page.
- W2287275630 abstract "The generalized symmetric eigenvalue problem (GSEVP) $A x = lambda B x$, $A$ symmetric, $B$ symmetric positive definite, occurs in many practical problems, but there is as yet no numerically stable algorithm which takes full advantage of its structure. The textit{standard method}(factor $B = G G^T$, solve the ordinary symmetric eigenvalue problem $G^{-1} A G^{-T} (G^T x) = lambda (G^T x)) is not numerically stable, while the backward stable $QZ$ algorithm takes no account of the special structure of the GSEVP. We show by example a previously unrecognizeddeficiency in the eigenvectors produced by the $QZ$ algorithm for some cases of this special class of problems. We suggest a new method that takes full advantage of the structure of the GSEVP yet appears not tosuffer from either the eigenvector deficiency of the $QZ$ algorithm, nor the lack of accuracy that can be introduced by the standard method when $B$ has a large condition number $kappa(B)$. The new method first reduces the problem to an equivalent one $A_c y = lambda D^{2}_{c} y$,$A_c$ symmetric, $D_c$ diagonal. It then implicitly applies Jacobi's method to $D^{-1}_{c} A_c D^{-1}_c$, while maintaining the symmetric and diagonal forms. The results of numerical tests indicate the benefits of this approach. A variant of the approach is amenable to parallel computation." @default.
- W2287275630 created "2016-06-24" @default.
- W2287275630 creator A5005540131 @default.
- W2287275630 creator A5025834032 @default.
- W2287275630 creator A5059509454 @default.
- W2287275630 date "1992-07-02" @default.
- W2287275630 modified "2023-09-27" @default.
- W2287275630 title "Solving the Generalized Symmetric Eigenvalue Problem" @default.
- W2287275630 hasPublicationYear "1992" @default.
- W2287275630 type Work @default.
- W2287275630 sameAs 2287275630 @default.
- W2287275630 citedByCount "0" @default.
- W2287275630 crossrefType "journal-article" @default.
- W2287275630 hasAuthorship W2287275630A5005540131 @default.
- W2287275630 hasAuthorship W2287275630A5025834032 @default.
- W2287275630 hasAuthorship W2287275630A5059509454 @default.
- W2287275630 hasConcept C11413529 @default.
- W2287275630 hasConcept C114614502 @default.
- W2287275630 hasConcept C121332964 @default.
- W2287275630 hasConcept C130367717 @default.
- W2287275630 hasConcept C134306372 @default.
- W2287275630 hasConcept C158693339 @default.
- W2287275630 hasConcept C192702615 @default.
- W2287275630 hasConcept C2524010 @default.
- W2287275630 hasConcept C2778113609 @default.
- W2287275630 hasConcept C28826006 @default.
- W2287275630 hasConcept C33923547 @default.
- W2287275630 hasConcept C45374587 @default.
- W2287275630 hasConcept C54848796 @default.
- W2287275630 hasConcept C62520636 @default.
- W2287275630 hasConceptScore W2287275630C11413529 @default.
- W2287275630 hasConceptScore W2287275630C114614502 @default.
- W2287275630 hasConceptScore W2287275630C121332964 @default.
- W2287275630 hasConceptScore W2287275630C130367717 @default.
- W2287275630 hasConceptScore W2287275630C134306372 @default.
- W2287275630 hasConceptScore W2287275630C158693339 @default.
- W2287275630 hasConceptScore W2287275630C192702615 @default.
- W2287275630 hasConceptScore W2287275630C2524010 @default.
- W2287275630 hasConceptScore W2287275630C2778113609 @default.
- W2287275630 hasConceptScore W2287275630C28826006 @default.
- W2287275630 hasConceptScore W2287275630C33923547 @default.
- W2287275630 hasConceptScore W2287275630C45374587 @default.
- W2287275630 hasConceptScore W2287275630C54848796 @default.
- W2287275630 hasConceptScore W2287275630C62520636 @default.
- W2287275630 hasLocation W22872756301 @default.
- W2287275630 hasOpenAccess W2287275630 @default.
- W2287275630 hasPrimaryLocation W22872756301 @default.
- W2287275630 hasRelatedWork W1458251719 @default.
- W2287275630 hasRelatedWork W1514155962 @default.
- W2287275630 hasRelatedWork W1540568927 @default.
- W2287275630 hasRelatedWork W1986541128 @default.
- W2287275630 hasRelatedWork W1991835897 @default.
- W2287275630 hasRelatedWork W2004556758 @default.
- W2287275630 hasRelatedWork W2007032864 @default.
- W2287275630 hasRelatedWork W2023565465 @default.
- W2287275630 hasRelatedWork W2024680604 @default.
- W2287275630 hasRelatedWork W2039078552 @default.
- W2287275630 hasRelatedWork W2078963121 @default.
- W2287275630 hasRelatedWork W2097507741 @default.
- W2287275630 hasRelatedWork W2134792818 @default.
- W2287275630 hasRelatedWork W2145806171 @default.
- W2287275630 hasRelatedWork W2265325209 @default.
- W2287275630 hasRelatedWork W2489164668 @default.
- W2287275630 hasRelatedWork W2775168820 @default.
- W2287275630 hasRelatedWork W2951371124 @default.
- W2287275630 hasRelatedWork W3177288072 @default.
- W2287275630 hasRelatedWork W2738193841 @default.
- W2287275630 isParatext "false" @default.
- W2287275630 isRetracted "false" @default.
- W2287275630 magId "2287275630" @default.
- W2287275630 workType "article" @default.