Journal of Fourier Analysis and Applications

, Volume 15, Issue 5, pp 706–722

A New Scheme for the Tensor Representation

Open AccessArticle

DOI: 10.1007/s00041-009-9094-9

Cite this article as:
Hackbusch, W. & Kühn, S. J Fourier Anal Appl (2009) 15: 706. doi:10.1007/s00041-009-9094-9


The paper presents a new scheme for the representation of tensors which is well-suited for high-order tensors. The construction is based on a hierarchy of tensor product subspaces spanned by orthonormal bases. The underlying binary tree structure makes it possible to apply standard Linear Algebra tools for performing arithmetical operations and for the computation of data-sparse approximations. In particular, a truncation algorithm can be implemented which is based on the standard matrix singular value decomposition (SVD) method.


Multilinear algebraTensor representationSingular value decomposition

Mathematics Subject Classification (2000)

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© Birkhäuser Boston 2009

Authors and Affiliations

  1. 1.MPI Mathematik in den NaturwissenschaftenLeipzigGermany