In this note we consider the problem of ParaTuck-2 decomposition of a three-way tensor.We provide an algebraic algorithm for finding the ParaTuck-2 decomposition for the case when the ParaTuck-2 ranks are smaller than the frontal dimensions of the tensors.Our approach relies only on linear algebra operations and is based on finding the kernel of a structured matrix constructed from the tensor.

翻译：本文考虑三阶张量的ParaTuck-2分解问题。针对ParaTuck-2秩小于张量正面维数的情况，我们提出了一种用于求解ParaTuck-2分解的代数算法。该方法仅依赖线性代数运算，其核心在于寻找由张量构建的结构化矩阵的零空间。