论文标题
低等级张量分解和近似值
Low Rank Tensor Decompositions and Approximations
论文作者
论文摘要
低等级张量的张量条目之间存在线性关系。这些线性关系可以用多线性多项式表示，这称为生成多项式。我们使用生成多项式来计算张量秩分解和低秩张量近似值。我们证明，如果给定的张量足够接近低级等级，则可以提供准最佳的低等级张量近似。
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.
