Some new estimations of diagonally dominant degree and eigenvalue inclusion sets for the Schur complement of block diagonally dominant matrices

Some new estimations of diagonally dominant degree and eigenvalue inclusion sets for the Schur complement of I(II)-block diagonally dominant matrices are given and it is proved that the new estimations on diagonally dominant degree are more accurate than those in [Liu et al., Theorems on Schur complement of block diagonally dominant matrices and their application in reducing the order for the solution of large scale linear systems, Linear Algebra Appl. 435 (2011), 3085–3100], and the new eigenvalue inclusion sets are contained in the sets given by liu et al.. Finally, a numerical example is given to illustrate the advantages of our results.

Website: http://www.arjonline.org/mathematics/american-research-journal-of-mathematics/