We present a rational empirical interpolation method for interpolating a family of parametrized functions to rational polynomials with invariant poles, leading to efficient numerical algorithms for space-fractional differential equations, parameter-robust preconditioning, and evaluation of matrix functions. Compared to classical rational approximation algorithms, the proposed method is more efficient for approximating a large number of target functions. In addition, we derive a convergence estimate of our rational approximation algorithm using the metric entropy numbers. Numerical experiments are included to demonstrate the effectiveness of the proposed method.

翻译：本文提出了一种有理经验插值方法，用于将参数化函数族插值为具有不变极点的有理多项式，从而为空间分数阶微分方程、参数鲁棒预条件处理以及矩阵函数求值等问题构建高效数值算法。与经典有理逼近算法相比，所提方法在逼近大量目标函数时具有更高效率。此外，我们利用度量熵数推导了该有理逼近算法的收敛性估计。数值实验验证了所提方法的有效性。