This paper presents a new method capable of reconstructing datasets with great precision and very low computational cost using a novel variant of the singular value decomposition (SVD) algorithm that has been named low-cost SVD (lcSVD). This algorithm allows to reconstruct a dataset from a minimum amount of points, that can be selected randomly, equidistantly or can be calculated using the optimal sensor placement functionality that is also presented in this paper, which finds minimizing the reconstruction error to validate the calculated sensor positions. This method also allows to find the optimal number of sensors, aiding users in optimizing experimental data recollection. The method is tested in a series of datasets, which vary between experimental and numerical simulations, two- and three-dimensional data and laminar and turbulent flow, have been used to demonstrate the capacity of this method based on its high reconstruction accuracy, robustness, and computational resource optimization. Maximum speed-up factors of 630 and memory reduction of 37\% are found when compared to the application of standard SVD to the dataset.

翻译：本文提出一种新方法，该方法通过奇异值分解算法的新型变体——低成本奇异值分解（lcSVD），能够以极低计算成本实现高精度数据集重构。该算法允许从可随机选取、等间距分布或通过本文提出的最优传感器布局功能计算的最小数量点中重构数据集，其中传感器布局功能通过最小化重构误差来验证计算出的传感器位置。该方法还能确定传感器最优数目，帮助用户优化实验数据采集。基于一系列实验与数值模拟、二维与三维数据以及层流与湍流数据集上的测试结果表明：该方法在重构精度、鲁棒性和计算资源优化方面具有显著能力。相比标准SVD处理数据集，该方法最高可实现630倍加速比和37%的内存缩减。