New Block Triangular Preconditioners for Saddle Point Linear Systems with Highly Singular (1,1) Blocks

摘要

We establish two types of block triangular preconditioners applied tothe linear saddle point problems with the singular (1,1) block. These preconditionersare based on the results presented in the paper of Rees andGreif (2007). We study thespectral characteristics of the preconditioners and show that all eigenvaluesof the preconditioned matrices are strongly clustered. The choice of theparameter is involved. Furthermore, we give the optimal parameter inpractical. Finally, numerical experiments are also reported for illustratingthe efficiency of the presented preconditioners.