论文标题
CP分解和反对称张量的低级别近似
CP decomposition and low-rank approximation of antisymmetric tensors
论文作者
论文摘要
对于反对称张量，该论文检查了一个低级别的近似值，该近似仅通过三个向量表示。我们描述了一种合适的低级格式，并提出了一种交替的最小二乘结构结构算法，用于查找这种近似值。此外，我们表明，这个近似问题等同于找到最佳的多线性低级反对称近似的问题，因此，等同于找到最佳的非结构性排名-1美元近似值的问题。还讨论了部分抗对称的情况。这些算法以朱莉娅的编程语言实现，并讨论了其数值性能。
For the antisymmetric tensors the paper examines a low-rank approximation which is represented via only three vectors. We describe a suitable low-rank format and propose an alternating least squares structure-preserving algorithm for finding such approximation. Moreover, we show that this approximation problem is equivalent to the problem of finding the best multilinear low-rank antisymmetric approximation and, consequently, equivalent to the problem of finding the best unstructured rank-$1$ approximation. The case of partial antisymmetry is also discussed. The algorithms are implemented in Julia programming language and their numerical performance is discussed.
