Eigenvalue localization refinements for the Schur complement

摘要

The theory of Schur complement plays an important role in many fields, as well as the theory of H-matrices. In this paper, we obtain some bounds for the eigenvalues of Schur complement by the entries of the original matrix instead of those of the Schur complement, for some special H-matrices. Also, we show how this result for a wider class can be applied for estimating bounds for the eigenvalues of Schur complement of an SDD matrix.