A class of strongly stable approximation for unbounded operators
Аммар Хеллаф, Sarra Benarab, Hamza Guebbaï, Wassim Merchela · Tambov University Reports Series Natural and Technical Sciences · 2019
We derive new sufficient conditions to solve the spectral pollution problem by using the generalized spectrum method. This problem arises in the spectral approximation when the approximate matrix may possess eigenvalues which are unrelated to any spectral properties of the original unbounded operator. We develop the theoretical background of the generalized spectrum method as well as illustrate its effectiveness with the spectral pollution. As a numerical application, we will treat the Schr¨odinger’s operator where the discretization process based upon the Kantorovich’s projection.