A block-diagonally preconditioned Uzawa splitting iteration method for solving a class of saddle-point problems

This paper develops a block diagonal preconditioned Uzawa splitting (BDP-US) method for solving saddle point problems by generalizing the Uzawa splitting iteration method proposed by Li and Ma (Numer Math Theory Methods Appl 2018; 11: 235-246). A sufficient condition is then provided to ensure the convergence of the BDP-US method. Meanwhile, a preconditioner on the basis of the BDP-US method is proposed, the spectral properties of the preconditioned matrix is analyzed, and the choice of the parameters for this matrix splitting iteration method is discussed. Numerical results are provided to support the obtained results, and demonstrate the effectiveness of BDP-US method as well as the corresponding preconditioner.