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=== In dynamical systems ===
The [[Koopman operator]] allows a finite-dimensional [[nonlinear system]] to be encoded as an infinite-dimensional [[linear system]]. In general, both of these problems are difficult to solve, but for the latter we can use the Ritz-Galerkin method to approximate a solution.<ref>{{cite arXiv|last1=Servadio|first1=Simone|last2=Arnas|first2=David|last3=Linares|first3=Richard|title=A Koopman Operator Tutorial with Orthogonal Polynomials|date=2021 |class=math.NA |eprint=2111.07485 }}</ref>
== The relationship with the finite element method ==
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