On eigenvalue bounds of two classes of two-by-two block indefinite matrices

Based on Theorem 2.1 of [Z.-Z. Bai, M.K. Ng, Z.-Q. Wang, Constraint preconditioners for symmetric indefinite matrices, SIAM J. Matrix Anal. Appl., 31 (2009), pp. 410–433] we present the eigenvalue bounds of two classes of two-by-two block indefinite matrices. Our results extend the existing ones about two-by-two block nonsingular and symmetric indefinite matrices with symmetric positive definite (1, 1) block. Numerical examples confirm that our estimated eigenvalue bounds are sharp and effective in practice.