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A systematic mathematical framework for the study of numerical algorithms would allow comparisons, facilitate conjugacy arguments, as well as enable the discovery of improved, accelerated, data-driven algorithms. Over the course of the last century, the Koopman operator has provided a mathematical framework for the study of dynamical systems, which facilitates conjugacy arguments and can provide efficient reduced descriptions. More recently, numerical approximations of the operator have made itarXiv:1907.10807v2 fatcat:dxtpyagjk5c2bcaijxljnczlwi