Linear Models from Proper Orthogonal Decomposition
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چکیده
Proper Orthogonal Decomposition (POD), alternatively known as Principal Component Analysis or the Karhunen-Loève decomposition, is a model-reduction technique which generates the optimal linear subspace of dimension D for a given set of higher-dimensional data. That is, if the data are contained within an attractor, the POD process can produce the affine linear space that best approximates the space containing that attractor. In this Chapter, I give a short derivation of the POD algorithm, then show the results from applying it to two different bistable atom-cavity regimes. For each regime, I show the performance of filters based on these POD results.
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