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@ARTICLE{DiNapoli:153312,
      author       = {Di Napoli, Edoardo and Fabregat-Traver, Diego and
                      Quintana-Ortí, Gregorio and Bientinesi, Paolo},
      title        = {{T}owards an efficient use of the {BLAS} library for
                      multilinear tensor contractions},
      journal      = {Applied mathematics and computation},
      volume       = {235},
      issn         = {0096-3003},
      address      = {New York, NY},
      publisher    = {Elsevier},
      reportid     = {FZJ-2014-02953},
      pages        = {454 - 468},
      year         = {2014},
      abstract     = {Mathematical operators whose transformation rules
                      constitute the building blocks of a multi-linear algebra are
                      widely used in physics and engineering applications where
                      they are very often represented as tensors. In the last
                      century, thanks to the advances in tensor calculus, it was
                      possible to uncover new research fields and make remarkable
                      progress in the existing ones, from electromagnetism to the
                      dynamics of fluids and from the mechanics of rigid bodies to
                      quantum mechanics of many atoms. By now, the formal
                      mathematical and geometrical properties of tensors are well
                      defined and understood; conversely, in the context of
                      scientific and high-performance computing, many
                      tensor-related problems are still open. In this paper, we
                      address the problem of efficiently computing contractions
                      among two tensors of arbitrary dimension by using kernels
                      from the highly optimized BLAS library. In particular, we
                      establish precise conditions to determine if and when GEMM,
                      the kernel for matrix products, can be used. Such conditions
                      take into consideration both the nature of the operation and
                      the storage scheme of the tensors, and induce a
                      classification of the contractions into three groups. For
                      each group, we provide a recipe to guide the users towards
                      the most effective use of BLAS.},
      cin          = {JSC},
      ddc          = {510},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {411 - Computational Science and Mathematical Methods
                      (POF2-411) / Simulation and Data Laboratory Quantum
                      Materials (SDLQM) (SDLQM)},
      pid          = {G:(DE-HGF)POF2-411 / G:(DE-Juel1)SDLQM},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000335898500047},
      doi          = {10.1016/j.amc.2014.02.051},
      url          = {https://juser.fz-juelich.de/record/153312},
}