Abstract
Linear operators allow for a structural analysis by their spectra and the related decomposition in stable linear subspaces. This does not apply to nonlinear operators, which are relevant for most natural phenomena. But this problem could be overcome. The nonlinear operator can induce a special linear operator in a large linear space. The induced linear operator is named Koopman operator offering structures to be mapped to the original settings. We try to give approaches for a numerical handling of some properties, generalizing the approach of the Dynamic Mode Decomposition of Peter Schmid.
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Küster, U. (2016). The Spectral Structure of a Nonlinear Operator and Its Approximation II. In: Resch, M., Bez, W., Focht, E., Patel, N., Kobayashi, H. (eds) Sustained Simulation Performance 2016. Springer, Cham. https://doi.org/10.1007/978-3-319-46735-1_7
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DOI: https://doi.org/10.1007/978-3-319-46735-1_7
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