An Improvement on Disc Separation of the Schur Complement and Bounds

Abstract

In this paper, we improve the disc separation of the Schur complement of strictly diagonally dominant matrices presented in Liu [SIAM. J. Matrix Anal. Appl., 27 (2005): 665-674]. As applications, we present some new bounds for determinants of original matrices and estimations for eigenvalues of Schur complement. By theoretical analysis, we improve the bounds of determinants established in Huang [Comput. Math. Appl., 50 (2005): 1677-1684].