Método POD y aplicaciones : caso discreto y continuo

Abstract

The proper orthogonal decomposition (POD) is a technique that aims at obtaining a compact representation of the data reducing the computational cost. The key idea of the POD is to reduce a large number of interdependent variables to a much smaller number of uncorrelated variables while retaining as much as possible of the variation in the original variables. This method has been gaining popularity over the years and it is being used to detect the number of signals in a multichannel time-series, for forecasting in meteorology or for the design of gurney flaps, among others. In this work, a theoretical study is carried out on this method in both the continuous and the discrete cases, the effective calculation is exposed and two numerical simulations are made; one for each of the two cases mentioned above.