Eigenvalue estimates of an indefinite block triangular preconditioner for saddle point problems

In this paper, an indefinite block triangular preconditioner for symmetric saddle point problems is discussed. The bounds for all the real eigenvalues of the preconditioned matrix are provided, and the bounds for the real and imaginary parts of all the complex eigenvalues of the preconditioned matrix are also provided. The corresponding theoretical results of paper by Bergamaschi (2012) are improved. Numerical experiments are reported to confirm our theoretical results.