, Volume 15, Issue 5, pp 706-722,
Open Access This content is freely available online to anyone, anywhere at any time.
Date: 22 Oct 2009

A New Scheme for the Tensor Representation

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.

Communicated by Reinhard Hochmuth.
Dedicated to the 60th birthday of Wolfgang Dahmen.