School of Applied Mathematics/Institue of Computational Science, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, China
Copyright © 2009 TingZhu Huang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We establish two types of block triangular preconditioners applied to the linear saddle point problems with the singular (1,1) block. These preconditioners are based on the results presented in the paper of Rees and Greif (2007). We study the spectral characteristics of the preconditioners and show that all eigenvalues of the preconditioned matrices are strongly clustered. The choice of the parameter is involved. Furthermore, we give the optimal parameter in
practical. Finally, numerical experiments are also reported for illustrating the efficiency of the presented preconditioners.