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, pp. 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 speed-up on large matrices and tensors.
翻译:我们提出一个新的快速随机算法,用于利用CountSketch对矩阵进行中间分解。然后,我们将这一方法扩大到Biagioni等人(J.Compuut.Phys.281,pp.116-134,2015年)提出的高压分解问题。为矩阵和高压设置提供理论性能保障。合成和真实数据的数值实验表明,我们的算法保持了竞争性方法的准确性,同时在较短的时间内运行,在大型矩阵和高压器上至少实现数量级加速。