We show that spectral data of the Koopman operator arising from an analytic expanding circle map $\tau$ can be effectively calculated using an EDMD-type algorithm combining a collocation method of order m with a Galerkin method of order n. The main result is that if $m \geq \delta n$, where $\delta$ is an explicitly given positive number quantifying by how much $\tau$ expands concentric annuli containing the unit circle, then the method converges and approximates the spectrum of the Koopman operator, taken to be acting on a space of analytic hyperfunctions, exponentially fast in n. Additionally, these results extend to more general expansive maps on suitable annuli containing the unit circle.

翻译：我们证明，由解析扩张圆映射$\tau$产生的Koopman算子的谱数据，可以通过结合阶数为m的配置方法与阶数为n的伽辽金方法的EDMD型算法有效计算。主要结论是：若$m \geq \delta n$，其中$\delta$是一个显式给定的正数，用以量化$\tau$对包含单位圆的同心环带的扩张程度，则该方法收敛，并以n的指数速度逼近Koopman算子（作用于解析超函数空间）的谱。此外，这些结果可推广到包含单位圆的适当环带上更一般的扩张映射。