Circular trichotomy of the spectrum of regular matrix pencils
This paper presents a method for approximating right and left deflating subspaces of regular matrix pencils corresponding to eigenvalues in, on and out the complex unit circle. This work is an extension of a previous one, where the condition that there are no eigenvalues on the unit circle is relaxed here. The method consists in the construction of two matrix sequences whose null spaces and the null space of their sum lead to approximations of the deflating subspaces corresponding to eigenvalues moduli according to the unit circle, and then an orthogonalization is used to obtain the corresponding deflating subspaces. The convergence analysis is done and some examples shows the validity of the proposed method.
scientific article; zbMATH DE number 5905226