We propose an iterative method to find pointwise growth exponential growth rates in linear problems posed on essentially one-dimensional domains. Such pointwise growth rates capture pointwise stability and instability in extended systems and arise as spectral values of a family of matrices that depends analytically on a spectral parameter, obtained via a scattering-type problem. Different from methods in the literature that rely on computing determinants of this nonlinear matrix pencil, we propose and analyze an inverse power method that allows one to locate robustly the closest spectral value to a given reference point in the complex plane. The method finds branch points, eigenvalues, and resonance poles without a priori knowledge.

翻译：我们建议一种迭接方法,在基本上一维的域上出现的线性问题中找到点增长指数增长率。这种点性增长率捕捉到扩展系统中的点性稳定性和不稳定性,并且作为一组矩阵的光谱值而产生,该矩阵的光谱值在分析上依赖于通过散射型问题获得的光谱参数。与文献中依赖计算非线性矩阵铅笔的决定因素的方法不同,我们建议并分析一种反向功率方法,这种方法可以使人们在复杂的平面上将最接近的光谱值定位到一个特定的参照点。该方法在没有先入之见的情况下找到分支点、电子价值和共振极。