Digital nets provide an efficient way to generate integration nodes of quasi-Monte Carlo (QMC) rules. For certain applications, as e.g. in Uncertainty Quantification, we are interested in obtaining a speed-up in computing products of a matrix with the vectors corresponding to the nodes of a QMC rule. In the recent paper "The fast reduced QMC matrix-vector product" (J. Comput. Appl. Math. 440, 115642, 2024), a speed up was obtained by using so-called reduced lattices and row reduced digital nets. In this work, we propose a different multiplication algorithm where we exploit the repetitive structure of column reduced digital nets instead of row reduced digital nets. This method has advantages over the previous one, as it facilitates the error analysis when using the integration nodes in a QMC rule. We also provide an upper bound for the quality parameter of column reduced digital nets, and numerical tests to illustrate the efficiency of the new algorithm.

翻译：数字网为生成拟蒙特卡罗（QMC）法则的积分节点提供了一种高效方法。在某些应用中，例如不确定性量化中，我们关注于加速计算矩阵与对应QMC法则节点的向量之间的乘积。在近期论文“快速约化QMC矩阵-向量乘积”（J. Comput. Appl. Math. 440, 115642, 2024）中，通过使用所谓的约化格点与行约化数字网实现了加速。在本工作中，我们提出了一种不同的乘法算法，该算法利用列约化数字网（而非行约化数字网）的重复结构。此方法相较于先前方法具有优势，因其在使用积分节点进行QMC法则计算时更便于误差分析。我们还给出了列约化数字网质量参数的一个上界，并通过数值实验验证了新算法的效率。