Sufficient regularity conditions for complex interval matrices and approximations of eigenvalues sets

Abstract

In this paper, two approaches are described to establish verifiable sufficient regularity conditions of complex interval matrices. In the first approach, a complex interval matrix is mapped to a real block interval matrix and then its sufficient regularity conditions are obtained. In the second approach, a necessary condition for the singularity of a complex interval matrix is derived and used to get its sufficient regularity conditions. As an application, the above derived sufficient regularity conditions are used to investigate the location of the outer approximations of individual eigenvalue sets of complex interval matrices. Two algorithms are proposed and results obtained are compared with those obtained by earlier methods and Monte Carlo simulations. The advantages of these algorithms are that they can detect gaps in between the approximations of the whole eigenvalue sets. The second algorithm is very effective compared to the first algorithm from the computational time point of view. Several numerical examples and statistical experiments are worked out to validate and demonstrate the efficacy of our work.