Inclusion sets for singular values Original Research Article

In this paper, the following inclusion sets are under certain conditions presented for singular values of a matrix image:imageandimagewhere ai=midaiimid and image for any iset membership, variant{1,2,cdots, three dots, centered,n}, ρ(B) and image denote the Perron root of the nonnegative matrix B=[bij] satisfying midaijmid,midajimidless-than-or-equals, slantbij for all i,jset membership, variant{1,2,cdots, three dots, centered,n} with i≠j and the set of all nontrivial circuits γ in Γ(A)—the associated directed digraph of A, respectively. Subsequently, relations between these two results are investigated. Theoretic analysis and numerical examples show that these estimates are more precise than recent corresponding results in some cases.