The digraphs and inclusion intervals of matrix singular values.

The paper investigates the inclusion intervals of matrix singular values. By employing the digraph of a matrix, some new inclusion intervals of matrix singular values are presented. These intervals are based mainly on the use of positive scale vectors and their intersections. Theoretic analysis and numerical examples show that these results improve and generalize some known results of Li et al. (Numer. Linear Algebra Appl. 2007; 14(2):115–128) and Kolotilina (J. Math. Sci. 2006; 137(3):4794–4800). Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]