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 21 articles , 1 standard article )

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  1. Lang, Bruno: Efficient reduction of banded Hermitian positive definite generalized eigenvalue problems to banded standard eigenvalue problems (2019)
  2. Rodríguez-Sánchez, Rafael; Catalán, Sandra; Herrero, José R.; Quintana-Ortí, Enrique S.; Tomás, Andrés E.: Look-ahead in the two-sided reduction to compact band forms for symmetric eigenvalue problems and the SVD (2019)
  3. Dongarra, Jack; Gates, Mark; Haidar, Azzam; Kurzak, Jakub; Luszczek, Piotr; Tomov, Stanimire; Yamazaki, Ichitaro: The singular value decomposition: anatomy of optimizing an algorithm for extreme scale (2018)
  4. Francisco, Juliano B.; Gonçalves, Douglas S.: A fixed-point method for approximate projection onto the positive semidefinite cone (2017)
  5. Aliaga, José I.; Alonso, Pedro; Badía, José M.; Chacón, Pablo; Davidović, Davor; López-Blanco, José R.; Quintana-Ortí, Enrique S.: A fast band-Krylov eigensolver for macromolecular functional motion simulation on multicore architectures and graphics processors (2016)
  6. Liao, Xiangke; Li, Shengguo; Cheng, Lizhi; Gu, Ming: An improved divide-and-conquer algorithm for the banded matrices with narrow bandwidths (2016)
  7. 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)
  8. Sukkari, Dalal; Ltaief, Hatem; Keyes, David: A high performance QDWH-SVD solver using hardware accelerators (2016)
  9. Araki, Sho; Kimura, Kinji; Yamamoto, Yusaku; Nakamura, Yoshimasa: Implementation details of an extended OQDS algorithm for singular values (2015)
  10. Ballard, G.; Carson, E.; Demmel, J.; Hoemmen, M.; Knight, N.; Schwartz, O.: Communication lower bounds and optimal algorithms for numerical linear algebra (2014)
  11. Ltaief, Hatem; Luszczek, Piotr; Dongarra, Jack: High-performance bidiagonal reduction using tile algorithms on homogeneous multicore architectures (2013)
  12. 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)
  13. Haidar, Azzam; Ltaief, Hatem; Dongarra, Jack: Toward a high performance tile divide and conquer algorithm for the dense symmetric eigenvalue problem (2012)
  14. Mori, Daisuke; Yamamoto, Yusaku: Backward error analysis of the AllReduce algorithm for Householder QR decomposition (2012)
  15. 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)
  16. Vömel, Christof; Tomov, Stanimire; Dongarra, Jack: Divide and conquer on hybrid GPU-accelerated multicore systems (2012)
  17. 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) ioport
  18. Ballard, Grey; Demmel, James; Holtz, Olga; Schwartz, Oded: Minimizing communication in numerical linear algebra (2011)
  19. Willems, Paul: On MR(^3)-type algorithms for the tridiagonal symmetric eigenproblem and bidiagonal SVD (2010)
  20. Bischof, Christian H.; Lang, Bruno; Sun, Xiaobai: Algorithm 807: The SBR toolbox -- software for successive band reduction. (2000)

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