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PARALLEL ALGORITHMS FOR COMPUTING THE TENSOR-TRAIN DECOMPOSITION.
- Source :
-
SIAM Journal on Scientific Computing . 2023, Vol. 45 Issue 3, pC101-C130. 30p. - Publication Year :
- 2023
-
Abstract
- The tensor-train (TT) decomposition expresses a tensor in a data-sparse format used in molecular simulations, high-order correlation functions, and optimization. In this paper, we propose four parallelizable algorithms that compute the TT format from various tensor inputs: (1) Parallel-TTSVD for traditional format, (2) PSTT and its variants for streaming data, (3) Tucker2TT for Tucker format, and (4) TT-fADI for solutions of Sylvester tensor equations. We provide theoretical guarantees of accuracy, parallelization methods, scaling analysis, and numerical results. For example, for a d-dimension tensor in Rn× ... × n, a two-sided sketching algorithm PSTT2 is shown to have a memory complexity of O (n d/2), improving upon O (nd 1) from previous algorithms. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10648275
- Volume :
- 45
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- SIAM Journal on Scientific Computing
- Publication Type :
- Academic Journal
- Accession number :
- 164774369
- Full Text :
- https://doi.org/10.1137/21M146079X