Low Rank Tensor Decompositions and Approximations
Numerical Analysis
2022-08-17 v1 Numerical Analysis
Abstract
There exist linear relations among tensor entries of low rank tensors. These linear relations can be expressed by multi-linear polynomials, which are called generating polynomials. We use generating polynomials to compute tensor rank decompositions and low rank tensor approximations. We prove that this gives a quasi-optimal low rank tensor approximation if the given tensor is sufficiently close to a low rank one.
Cite
@article{arxiv.2208.07477,
title = {Low Rank Tensor Decompositions and Approximations},
author = {Jiawang Nie and Li Wang and Zequn Zheng},
journal= {arXiv preprint arXiv:2208.07477},
year = {2022}
}