A Riesz-projection-based method for nonlinear eigenvalue problems

We propose an algorithm for general nonlinear eigenvalue problems to compute eigenvalues within a chosen contour and to compute the corresponding eigenvectors. 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. No auxiliary functions have to be introduced for linearization. The numerical implementation of the approach is straightforward and the algorithm allows for parallelization. We apply the method to two examples from physics. Resonant states of a one-dimensional quantum mechanical system and resonant states of a three-dimensional photonic nanoantenna are computed.

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