A new scheme for the tensor representation

Wolfgang Hackbusch and Stefan Kühn

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Submission date: 07. Jan. 2009
Pages: 16
published in: The journal of Fourier analysis and applications, 15 (2009) 5, p. 706-722 
DOI number (of the published article): 10.1007/s00041-009-9094-9
Bibtex
MSC-Numbers: 15A69, 65F99
Keywords and phrases: tensor representation, tensor calculus
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Abstract:
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.