论文标题
L-DEIM诱导的高阶张量插值分解
An L-DEIM Induced High Order Tensor Interpolatory Decomposition
论文作者
论文摘要
本文根据离散的经验插值方法的新变体（称为l-deim）得出了塔克格式中张量的cur型分解。这种新颖的采样技术使我们能够构建一种用于计算结构保存分解的有效算法，从而大大降低了计算成本。对于大型数据集，我们将随机抽样技术与L-DEIM程序结合在一起，以进一步提高效率。此外，我们提出了用于计算混合分解的随机算法，该算法比张量验证分解得出可解释的分解并提供了较小的近似误差。我们提供了与我们提出的算法相关的概率错误的全面分析，并提出了证明我们方法有效性的数值结果。
This paper derives the CUR-type factorization for tensors in the Tucker format based on a new variant of the discrete empirical interpolation method known as L-DEIM. This novel sampling technique allows us to construct an efficient algorithm for computing the structure-preserving decomposition, which significantly reduces the computational cost. For large-scale datasets, we incorporate the random sampling technique with the L-DEIM procedure to further improve efficiency. Moreover, we propose randomized algorithms for computing a hybrid decomposition, which yield interpretable factorization and provide a smaller approximation error than the tensor CUR factorization. We provide comprehensive analysis of probabilistic errors associated with our proposed algorithms, and present numerical results that demonstrate the effectiveness of our methods.
