We show that spectral data of transfer operators given by holomorphic data can be approximated using an effective numerical scheme based on Lagrange interpolation. In particular, we show that for one-dimensional systems satisfying certain complex contraction properties, spectral data of the approximants converge exponentially to the spectral data of the transfer operator with the exponential rate determined by the respective complex contraction ratios of the underlying systems. We demonstrate the effectiveness of this scheme by numerically computing eigenvalues of transfer operators arising from interval and circle maps, as well as Lyapunov exponents of (positive) random matrix products and iterated function systems, based on examples taken from the literature.

中文翻译：

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与全纯数据相关的传递算子的拉格朗日近似

我们表明，可以使用基于拉格朗日插值的有效数值方案来近似由全纯数据给出的传递算子的谱数据。特别是，我们表明，对于满足某些复收缩特性的一维系统，近似值的谱数据以指数方式收敛到传递算子的谱数据，其指数速率由基础系统的相应复收缩率决定。我们根据文献中的例子，通过数值计算由区间和圆图产生的传递算子的特征值，以及（正）随机矩阵乘积和迭代函数系统的 Lyapunov 指数，证明了该方案的有效性。