SVD enclosure of a class of interval matrices

Abstract

This paper develops the concept of the singular value decomposition (SVD) of a class of interval matrices. The methodology relies on tighter outer estimations of eigenvalues and their corresponding eigenvectors of an interval matrix. The interval enclosure of every eigenvalue of an interval matrix is determined using an iterative procedure, and an algorithm is proposed for determining the corresponding eigenvector enclosure. Using these concepts, the SVD enclosure of an interval matrix is obtained. Numerical examples are provided to demonstrate the principles of the proposed methodologies at different stages.