# Low Rank Tensor Decompositions and Approximations

@article{Nie2022LowRT, title={Low Rank Tensor Decompositions and Approximations}, author={Jiawang Nie and L. xilinx Wang and Zequn Zheng}, journal={ArXiv}, year={2022}, volume={abs/2208.07477} }

. There exist linear relations among tensor entries of low rank ten- sors. 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.

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