New inclusion sets for singular values

Abstract

In this paper, for a given matrix , in terms of and , where , , some new inclusion sets for singular values of the matrix are established. It is proved that the new inclusion sets are tighter than the Geršgorin-type sets (Qi in Linear Algebra Appl. 56:105-119, 1984) and the Brauer-type sets (Li in Comput. Math. Appl. 37:9-15, 1999). A numerical experiment shows the efficiency of our new results.

An S-type singular value inclusion set for rectangular tensors

“…For example, the elasticity tensor is a tensor with and or 3; for details, see [ 1 ]. Due to the fact that singular values of rectangular tensors have a wide range of practical applications in the strong ellipticity condition problem in solid mechanics [ 5 , 6 ] and the entanglement problem in quantum physics [ 7 , 8 ], very recently, it has attracted attention of researchers [ 9 – 17 ]. Chang et al .…”