We propose a new fast randomized algorithm for interpolative decomposition of matrices which utilizes CountSketch. We then extend this approach to the tensor interpolative decomposition problem introduced by Biagioni et al. (J. Comput. Phys. 281(C), 116–134 (2015)). Theoretical performance guarantees are provided for both the matrix and tensor settings. Numerical experiments on both synthetic and real data demonstrate that our algorithms maintain the accuracy of competing methods, while running in less time, achieving at least an order of magnitude speedup on large matrices and tensors.

中文翻译：

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使用CountSketch的快速随机矩阵和张量插值分解

我们提出了一种新的利用CountSketch进行矩阵插值分解的快速随机算法。然后，我们将此方法扩展到Biagioni等人引入的张量插值分解问题。（J.计算物理281（C），116-134（2015））。为矩阵和张量设置提供了理论上的性能保证。在合成数据和真实数据上的数值实验表明，我们的算法可保持竞争方法的准确性，同时运行时间更短，在大型矩阵和张量上的速度至少提高了一个数量级。