  We present a practical and effective method for rigorously estimating
quantities associated to top eigenvalues of transfer operators to very high
precision. The method combines explicit error bounds of the Lagrange-Chebyshev
approximation with an established min-max method. We illustrate its
applicability by significantly improving rigorous estimates on various ergodic
quantities associated to the Bolyai-R\'enyi map.

Dynamical Systems;Numerical Analysis;Numerical Analysis