The Numerical Approximation of Koopman Modes of a Nonlinear Operator Along a Trajectory
U. Küster, R. Schneider, and A. Ruopp. Sustained Simulation Performance 2017, page 27--51. Cham, Springer International Publishing, (2017)
Abstract
The spectral theory of linear operators enables the analysis of their properties on stable subspaces. The Koopman operator allows to extend these approaches to a large class of nonlinear operators in a surprising way. This is even applicable for numerical analysis of time dependent data of simulations and measurements. We give here some remarks on the numerical approach, link it to spectral analysis by the Herglotz-Bochner theorem and are doing some steps for significance for partial differential equations.
%0 Conference Paper
%1 10.1007/978-3-319-66896-3_3
%A Küster, Uwe
%A Schneider, Ralf
%A Ruopp, Andreas
%B Sustained Simulation Performance 2017
%C Cham
%D 2017
%E Resch, Michael M.
%E Bez, Wolfgang
%E Focht, Erich
%E Gienger, Michael
%E Kobayashi, Hiroaki
%I Springer International Publishing
%K hlrs hpc myown
%P 27--51
%T The Numerical Approximation of Koopman Modes of a Nonlinear Operator Along a Trajectory
%X The spectral theory of linear operators enables the analysis of their properties on stable subspaces. The Koopman operator allows to extend these approaches to a large class of nonlinear operators in a surprising way. This is even applicable for numerical analysis of time dependent data of simulations and measurements. We give here some remarks on the numerical approach, link it to spectral analysis by the Herglotz-Bochner theorem and are doing some steps for significance for partial differential equations.
%@ 978-3-319-66896-3
@inproceedings{10.1007/978-3-319-66896-3_3,
abstract = {The spectral theory of linear operators enables the analysis of their properties on stable subspaces. The Koopman operator allows to extend these approaches to a large class of nonlinear operators in a surprising way. This is even applicable for numerical analysis of time dependent data of simulations and measurements. We give here some remarks on the numerical approach, link it to spectral analysis by the Herglotz-Bochner theorem and are doing some steps for significance for partial differential equations.},
added-at = {2021-09-28T11:21:21.000+0200},
address = {Cham},
author = {K{\"u}ster, Uwe and Schneider, Ralf and Ruopp, Andreas},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/20b6ca4808f381e80d5b17023457bdcfe/ralfschneider},
booktitle = {Sustained Simulation Performance 2017 },
editor = {Resch, Michael M. and Bez, Wolfgang and Focht, Erich and Gienger, Michael and Kobayashi, Hiroaki},
interhash = {55ecd6e672ffbc3993ac7acf60ff9d97},
intrahash = {0b6ca4808f381e80d5b17023457bdcfe},
isbn = {978-3-319-66896-3},
keywords = {hlrs hpc myown},
pages = {27--51},
publisher = {Springer International Publishing},
timestamp = {2021-09-28T09:31:04.000+0200},
title = {The Numerical Approximation of Koopman Modes of a Nonlinear Operator Along a Trajectory},
year = 2017
}
