A New Look at Proper Orthogonal Decomposition

@article{Rathinam2003ANL,
  title={A New Look at Proper Orthogonal Decomposition},
  author={Muruhan Rathinam and Linda R. Petzold},
  journal={SIAM J. Numer. Anal.},
  year={2003},
  volume={41},
  pages={1893-1925}
}
We investigate some basic properties of the proper orthogonal decomposition (POD) method as it is applied to data compression and model reduction of finite dimensional nonlinear systems. First we provide an analysis of the errors involved in solving a nonlinear ODE initial value problem using a POD reduced order model. Then we study the effects of small perturbations in the ensemble of data from which the POD reduced order model is constructed on the reduced order model. We explain why in some… 
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