A note on block-diagonally preconditioned PIU methods for singular saddle point problems

Abstract

Recently, Bai and Wang [On parameterized inexact Uzawa methods for generalized saddle point problems, Linear Algebra Appl. 428 (2008), pp. 2900–2932] and Gao and Kong [Block diagonally preconditioned PIU methods of saddle point problems, Appl. Math. Comput. 216 (2010), pp. 1880–1887] discussed the parameterized inexact Uzawa (PIU) method and the preconditioned parameterized inexact Uzawa (PPIU) method. In this paper, we further study the block-diagonally preconditioned PIU methods for solving singular saddle point problems, and give the corresponding convergence analysis.

Keywords:

• singular linear systems
• saddle point problems
• PPIU method
• convergence

2000 AMS Subject Classifications :

• 65F10
• 15A09

Acknowledgements

The authors would like to thank Dr. Qin Sheng, and two referees for their very detailed comments which greatly improved the presentation of this paper. This work is supported by Zhejiang Provincial National Science Foundation of China under Grant No. Y1110451.