Look-ahead in the two-sided reduction to compact band forms for symmetric eigenvalue problems and the SVD

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 seco...

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Veröffentlicht in:Numerical algorithms Jg. 80; H. 2; S. 635 - 660
Hauptverfasser: Rodríguez-Sánchez, Rafael, Catalán, Sandra, Herrero, José R., Quintana-Ortí, Enrique S., Tomás, Andrés E.
Format: Journal Article Verlag
Sprache:Englisch
Veröffentlicht: New York Springer US 01.02.2019
Springer Nature B.V
Schlagworte:
Algebra
Algebras, Linear
Algorithms
Bandwidths
Computer Science
Critical path
Decomposition
Eigenvalues
Informàtica
Informàtica teòrica
Linear algebra
Look-ahead
Matrices
Matrius (Matemàtica)
Numeric Computing
Numerical Analysis
Original Paper
Reduction
Singular value decomposition
Symmetric eigenvalue problems
Theory of Computation
Two-sided reduction to compact band form
Àlgebra lineal
Àrees temàtiques de la UPC
Look-ahead
Symmetric eigenvalue problems
Two-sided reduction to compact band form
Singular value decomposition
ISSN:1017-1398, 1572-9265
Online-Zugang:Volltext
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Beschreibung
Zusammenfassung: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 look-ahead, 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.
Bibliographie:ObjectType-Article-1
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-018-0500-8