We propose an algorithm for general nonlinear eigenvalue problems to compute physically relevant eigenvalues within a chosen contour. Eigenvalue information is explored by contour integration incorporating different weight functions. The gathered information is processed by solving a nonlinear system of equations of small dimension prioritizing eigenvalues with high physical impact. No auxiliary functions have to be introduced since linearization is not used. The numerical implementation is straightforward as the evaluation of the integrand can be regarded as a blackbox. We apply the method to a quantum mechanical problem and to two nanophotonic systems.

中文翻译：

---

非线性特征值问题的基于Riesz投影的方法

我们提出了一种针对一般非线性特征值问题的算法，以计算选定轮廓内与物理相关的特征值。特征值信息通过结合不同权重函数的轮廓积分进行探索。通过求解一个非线性的小维方程组来处理收集的信息，该系统优先考虑具有较高物理影响的特征值。由于不使用线性化，因此无需引入辅助功能。数值实现很简单，因为对被积物的评估可以看作是黑盒。我们将该方法应用于量子力学问题和两个纳米光子系统。