title: New inclusion sets for singular values.
abstract: In this paper, for a given matrix [Formula: see text], in terms of [Formula: see text] and [Formula: see text], where [Formula: see text], [Formula: see text], 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.
authors.affiliation: School of Mathematics, Zunyi Normal College, Zunyi, Guizhou 563006 P.R. China.
authors.forename: Jun
authors.initials: J
authors.lastname: He
authors.affiliation: School of Mathematics, Zunyi Normal College, Zunyi, Guizhou 563006 P.R. China.
authors.forename: Yan-Min
authors.initials: YM
authors.lastname: Liu
authors.affiliation: School of Mathematics, Zunyi Normal College, Zunyi, Guizhou 563006 P.R. China.
authors.forename: Jun-Kang
authors.initials: JK
authors.lastname: Tian
authors.affiliation: School of Mathematics, Zunyi Normal College, Zunyi, Guizhou 563006 P.R. China.
authors.forename: Ze-Rong
authors.initials: ZR
authors.lastname: Ren
keywords: inclusion sets; matrix; singular value