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We show that spectral data of transfer operators given by holomorphic datacan be approximated using an effective numerical scheme based on Lagrangeinterpolation. In particular, we show that for one-dimensional systemssatisfying certain complex contraction properties, spectral data of theapproximants converge exponentially to the spectral data of the transferoperator with the exponential rate determined by the respective complexcontraction ratios of the underlying systems. We demonstrate the effectivenessof this scheme by numerically computing eigenvalues of transfer operatorsarising from interval and circle maps, as well as Lyapunov exponents of(positive) random matrix products and iterated function systems, based onexamples taken from the literature.

Lagrange approximation of transfer operators associated with holomorphic data