Look-ahead in the two-sided reduction to compact band forms for symmetric eigenvalue problems and the SVD
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Otros documentos de la autoría: Rodríguez Sánchez, Rafael; Catalán, Sandra; Herrero, José R.; Quintana-Orti, Enrique S.; Tomás Domínguez, Andrés Enrique
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Título
Look-ahead in the two-sided reduction to compact band forms for symmetric eigenvalue problems and the SVDAutoría
Fecha de publicación
2019Editor
Springer VerlagISSN
1017-1398; 1572-9265Cita bibliográfica
Rodríguez-Sánchez, R., Catalán, S., Herrero, J.R. et al. Numer Algor (2019) 80: 635. https://doi.org/10.1007/s11075-018-0500-8Tipo de documento
info:eu-repo/semantics/articleVersión de la editorial
https://link.springer.com/article/10.1007/s11075-018-0500-8Versión
info:eu-repo/semantics/submittedVersionPalabras clave / Materias
Resumen
We address the reduction to compact band forms, via unitary similarity
transformations, for the solution of symmetric eigenvalue problems and the computation of the singular value decomposition (SVD). Concretely, in ... [+]
We address the reduction to compact band forms, via unitary similarity
transformations, for the solution of symmetric eigenvalue problems and the computation of the singular value decomposition (SVD). Concretely, in the first case, we
revisit the reduction to symmetric band form, while, for the second case, we propose a similar alternative, which transforms the original matrix to (unsymmetric)
band form, replacing the conventional reduction method that produces a triangular–
band output. In both cases, we describe algorithmic variants of the standard Level
3 Basic Linear Algebra Subroutines (BLAS)-based procedures, enhanced with lookahead, to overcome the performance bottleneck imposed by the panel factorization.
Furthermore, our solutions employ an algorithmic block size that differs from the
target bandwidth, illustrating the important performance benefits of this decision.
Finally, we show that our alternative compact band form for the SVD is key to introduce an effective look-ahead strategy into the corresponding reduction procedure. [-]
Publicado en
Numerical Algorithms February, 2019, Volume 80, Issue 2.Proyecto de investigación
TIN2014-53495-R ; TIN2015-65316-P ; 2014-SGR-1051 ; 732631 OPRECOMPDerechos de acceso
© Springer Science+Business Media, LLC, part of Springer Nature 2018.
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