On the Eigenvalues Distribution of Preconditioned Block Two-by-two Matrix.

The spectral properties of a class of block 2x2 matrix are studied, which arise in the numercial solutions of PDE-constrained optimization problems. Based on the Schur complement approximate approach and inexact Uzawa preconditioner, the eigenvalues distribution of preconditioned matrix is discussed by the similarity transformation. Moreover, The numerical experiments originated in PDE-constrained optimization problem are presented to show that the theoretical bound of the eigenvalues is in good agreement with its practical bound. [ABSTRACT FROM AUTHOR]