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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
2/2009

A new scheme for the tensor representation

Wolfgang Hackbusch and Stefan Kühn

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.

Received:
Jan 7, 2009
Published:
Jan 7, 2009
MSC Codes:
15A69, 65F99
Keywords:
tensor representation, tensor calculus

Related publications

inJournal
2009 Journal Open Access
Wolfgang Hackbusch and Stefan Kühn

A new scheme for the tensor representation

In: The journal of Fourier analysis and applications, 15 (2009) 5, pp. 706-722