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This paper presents a new method capable of reconstructing datasets withgreat precision and very low computational cost using a novel variant of thesingular value decomposition (SVD) algorithm that has been named low-cost SVD(lcSVD). This algorithm allows to reconstruct a dataset from a minimum amountof points, that can be selected randomly, equidistantly or can be calculatedusing the optimal sensor placement functionality that is also presented in thispaper, which finds minimizing the reconstruction error to validate thecalculated sensor positions. This method also allows to find the optimal numberof sensors, aiding users in optimizing experimental data recollection. Themethod is tested in a series of datasets, which vary between experimental andnumerical simulations, two- and three-dimensional data and laminar andturbulent flow, which have been used to demonstrate the capacity of this methodbased on its high reconstruction accuracy, robustness, and computationalresource optimization. Maximum speed-up factors of 630 and memory reduction of37% 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.

Low-cost singular value decomposition with optimal sensor placement