We describe a strategy for solving nonlinear eigenproblems numerically. Our approach is based on the approximation of a vector-valued function, defined as solution of a non-homogeneous version of the eigenproblem. This approximation step is carried out via the minimal rational interpolation method. Notably, an adaptive sampling approach is employed: the expensive data needed for the approximation is gathered at locations that are optimally chosen by following a greedy error indicator. This allows the algorithm to employ computational resources only where "most of the information" on not-yet-approximated eigenvalues can be found. Then, through a post-processing of the surrogate, the sought-after eigenvalues and eigenvectors are recovered. Numerical examples are used to showcase the effectiveness of the method.

翻译：我们用数字描述一种解决非线性电子元问题的战略。 我们的方法基于矢量值函数的近似值, 定义为非同质版本的异质问题的解决办法。 这个近似步骤是通过最低合理内插方法进行的。 值得注意的是, 采用了适应性抽样方法: 近似所需的昂贵数据是在贪婪误差指标所最佳选择的地点收集的。 这允许算法仅在找到“ 大部分信息” 有关非现近似电子元值的“ 大部分信息” 的情况下才使用计算资源。 然后, 通过对代管进行后处理, 回收了所寻求的电子元值和源源数。 使用数字实例来展示该方法的有效性 。