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MiS Preprint

A new scheme for the tensor representation

Wolfgang Hackbusch and Stefan Kühn


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.

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

Related publications

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