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Volume 2, Issue 4
Preservation of Linear Constraints in Approximation of Tensors

Eugene Tyrtyshnikov

DOI: 10.4208/nmtma.2009.m9004s

Numer. Math. Theor. Meth. Appl., 2 (2009), pp. 421-426.

Published online: 2009-02

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  • Abstract

For an arbitrary tensor (multi-index array) with linear constraints at each direction, it is proved that the factors of any minimal canonical tensor approximation to this tensor satisfy the same linear constraints for the corresponding directions.

  • Keywords

Multi-index arrays, tensors, linear constraints, low rank approximation, canonical tensor decomposition, multilevel matrices.

  • AMS Subject Headings

15A12, 65F10, 65F15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-2-421, author = {Eugene Tyrtyshnikov}, title = {Preservation of Linear Constraints in Approximation of Tensors}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2009}, volume = {2}, number = {4}, pages = {421--426}, abstract = {

For an arbitrary tensor (multi-index array) with linear constraints at each direction, it is proved that the factors of any minimal canonical tensor approximation to this tensor satisfy the same linear constraints for the corresponding directions.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2009.m9004s}, url = {http://global-sci.org/intro/article_detail/nmtma/6032.html} }
TY - JOUR T1 - Preservation of Linear Constraints in Approximation of Tensors AU - Eugene Tyrtyshnikov JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 421 EP - 426 PY - 2009 DA - 2009/02 SN - 2 DO - http://doi.org/10.4208/nmtma.2009.m9004s UR - https://global-sci.org/intro/article_detail/nmtma/6032.html KW - Multi-index arrays, tensors, linear constraints, low rank approximation, canonical tensor decomposition, multilevel matrices. AB -

For an arbitrary tensor (multi-index array) with linear constraints at each direction, it is proved that the factors of any minimal canonical tensor approximation to this tensor satisfy the same linear constraints for the corresponding directions.

Eugene Tyrtyshnikov. (2009). Preservation of Linear Constraints in Approximation of Tensors. Numerical Mathematics: Theory, Methods and Applications. 2 (4). 421-426. doi:10.4208/nmtma.2009.m9004s
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