A new scheme for the tensor representation
Wolfgang Hackbusch and Stefan Kühn
Contact the author: Please use for correspondence this email.
Submission date: 07. Jan. 2009
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
MSC-Numbers: 15A69, 65F99
Keywords and phrases: tensor representation, tensor calculus
Download full preprint: PDF (202 kB), PS ziped (217 kB)
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.