Eigenvalue bounds and Perron-Frobenius theory for nonnegative or positive interval matrices

Abstract

This paper introduces two classes of regular interval matrices and establishes intervals that either include or exclude the real eigenvalues of positive interval matrices. The Perron-Frobenius theory is extended to the generalized interval eigenvalue problem for nonnegative interval matrices under certain conditions. Moreover, necessary and sufficient conditions are derived for the existence of a real scalar and a positive vector that satisfy the generalized interval eigenvalue problem for nonnegative interval matrices under certain conditions.