  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, which 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.
This method will be incorporated into ModelFLOWs-app's next version release.
