The paper introduces a hybrid approach to the CUR-type decomposition of tensors in the Tucker format. The idea of the hybrid algorithm is to write a tensor \({\mathscr {X}}\) as a product of a core tensor \({\mathscr {S}}\), a matrix C obtained by extracting mode-k fibers of \({\mathscr {X}}\), and matrices \(Z_j\), \(j=1,\ldots ,k-1,k+1,\ldots ,d\), chosen to minimize the approximation error. The approximation can easily be modified to preserve the fibers in more than one mode. The approximation error obtained this way is smaller than the one from the standard tensor CUR-type method. This difference increases as the tensor dimension increases. It also increases as the number of modes in which the original fibers are preserved decreases.

本文介绍了一种混合方法，用于以Tucker格式对张量进行CUR类型分解。混合算法的思想是写一个张量\（{\ mathscr {X}} \）作为核心张量\ {{\ mathscr {S}} \\}的乘积，这是通过提取模式k获得的矩阵C。\（{\ mathscr {X}} \）和矩阵\（Z_j \），\（j = 1，\ ldots，k-1，k + 1，\ ldots，d \）的纤维选择用于最小化近似误差。可以轻松修改近似值，以使光纤保持不止一种模式。通过这种方法获得的逼近误差小于标准张量CUR类型方法的逼近误差。随着张量维数的增加，此差异也会增加。随着保存原始纤维的模式数量减少，它也会增加。