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Numerical Mathematics and Advanced Applications - ENUMATH 2013 pp 315–323Cite as

Tensor Formats Based on Subspaces are Positively Invariant Sets for Laplacian-Like Dynamical Systems

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Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 103))

Abstract

In this note, we show that the set of tensors with bounded rank are positively invariant sets for linear evolution equations defined by Laplacian-like operators. In consequence, once a trajectory of the system enters to this class of set, it will never leave it again.

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Author information

Authors and Affiliations

  1. Departamento de Ciencias, Físicas, Matemáticas y de la Computación, Universidad CEU Cardenal Herrera, San Bartolomé 55, 46115, Alfara del Patriarca, Valencia, Spain

    Antonio Falcó

Authors
  1. Antonio Falcó
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Corresponding author

Correspondence to Antonio Falcó .

Editor information

Editors and Affiliations

  1. MATHICSE-ANMC, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Assyr Abdulle

  2. SB MATHICSE CMCS, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Simone Deparis

  3. SB MATHICSE ANCHP, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Daniel Kressner

  4. SB MATHICSE CSQI, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Fabio Nobile

  5. SB MATHICSE GR-PI, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Marco Picasso

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Falcó, A. (2015). Tensor Formats Based on Subspaces are Positively Invariant Sets for Laplacian-Like Dynamical Systems. In: Abdulle, A., Deparis, S., Kressner, D., Nobile, F., Picasso, M. (eds) Numerical Mathematics and Advanced Applications - ENUMATH 2013. Lecture Notes in Computational Science and Engineering, vol 103. Springer, Cham. https://doi.org/10.1007/978-3-319-10705-9_31

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