SBR Toolbox

Algorithm 807: The SBR Toolbox—software for successive band reduction. We present a software toolbox for symmetric band reduction via orthogonal transformations, together with a testing and timing program. The toolbox contains drivers and computational routines for the reduction of full symmetric matrices to banded form and the reduction of banded matrices to narrower banded or tridiagonal form, with optional accumulation of the orthogonal transformations, as well as repacking routines for storage rearrangement. The functionality and the calling sequences of the routines are described, with a detailed discussion of the “control” parameters that allow adaptation of the codes to particular machine and matrix characteristics. We also briefly describe the testing and timing program included in the toolbox.

This software is also peer reviewed by journal TOMS.


References in zbMATH (referenced in 9 articles )

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  1. Shao, Meiyue; da Jornada, Felipe H.; Yang, Chao; Deslippe, Jack; Louie, Steven G.: Structure preserving parallel algorithms for solving the Bethe-Salpeter eigenvalue problem (2016)
  2. Ltaief, Hatem; Luszczek, Piotr; Dongarra, Jack: High-performance bidiagonal reduction using tile algorithms on homogeneous multicore architectures (2013)
  3. Aliaga, José I.; Bientinesi, Paolo; Davidović, Davor; Di Napoli, Edoardo; Igual, Francisco D.; Quintana-Ortí, Enrique S.: Solving dense generalized eigenproblems on multi-threaded architectures (2012)
  4. Haidar, Azzam; Ltaief, Hatem; Dongarra, Jack: Toward a high performance tile divide and conquer algorithm for the dense symmetric eigenvalue problem (2012)
  5. Mori, Daisuke; Yamamoto, Yusaku: Backward error analysis of the AllReduce algorithm for Householder QR decomposition (2012)
  6. Van Zee, Field G.; van de Geijn, Robert A.; Quintana-Ortí, Gregorio; Elizondo, G.Joseph: Families of algorithms for reducing a matrix to condensed form (2012)
  7. Vömel, Christof; Tomov, Stanimire; Dongarra, Jack: Divide and conquer on hybrid GPU-accelerated multicore systems (2012)
  8. Auckenthaler, T.; Blum, V.; Bungartz, H.-J.; Huckle, T.; Johanni, R.; Krämer, L.; Lang, B.; Lederer, H.; Willems, P.R.: Parallel solution of partial symmetric eigenvalue problems from electronic structure calculations (2011)
  9. Ballard, Grey; Demmel, James; Holtz, Olga; Schwartz, Oded: Minimizing communication in numerical linear algebra (2011)