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.

翻译：我们提出了一种实用且有效的方法，用于严格估计转移算子主特征值相关量至高精度。该方法将拉格朗日-切比雪夫逼近的显式误差界与已有的极大极小方法相结合。通过显著改进与玻尔亚伊-雷尼映射相关的若干遍历量的严格估计，我们阐释了该方法的适用性。