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A New Scheme for the Tensor Representation
Open accessAbstract
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.
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Citations
Cited by
Oseledets, I. V. (2011) · SIAM Journal on Scientific Computing · doi:10.1137/090752286 · Cited by 2,636
The ITensor Software Library for Tensor Network Calculations
Fishman, M., White, S., & Stoudenmire, E. M. (2022) · SciPost Physics Codebases · doi:10.21468/scipostphyscodeb.4 · Cited by 1,084
Quantum Algorithms for Quantum Chemistry and Quantum Materials Science
Bauer, B., Bravyi, S., Motta, M., & Chan, G. K.-L. (2020) · Chemical Reviews · doi:10.1021/acs.chemrev.9b00829 · Cited by 848
A literature survey of low‐rank tensor approximation techniques
Grasedyck, L., Kressner, D., & Tobler, C. (2013) · GAMM-Mitteilungen · doi:10.1002/gamm.201310004 · Cited by 577
Towards quantum machine learning with tensor networks
Huggins, W., Patil, P., Mitchell, B., Whaley, K. B., & Stoudenmire, E. M. (2019) · Quantum Science and Technology · doi:10.1088/2058-9565/aaea94 · Cited by 366
Metadata
- Authors
- Hackbusch, W., & Kühn, S.
- Venue
- Journal of Fourier Analysis and Applications
- Published
- 2009-10
- Volume
- 15
- Issue
- 5
- Pages
- 706-722
- ISSN
- 1069-5869 (ISSN-L)
- 1531-5851
- OpenAlex
- W2088025933
- Cited by
- 453
- References
- 0
- FWCI
- 3.81
- Type
- journal article
- Language
- en
- Open access
- hybrid
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- Hackbusch, W., & Kühn, S. (2009). A New Scheme for the Tensor Representation. Journal of Fourier Analysis and Applications. https://doi.org/10.1007/s00041-009-9094-9
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
