On augmentation block triangular preconditioners for regularized saddle point problems

Two augmentation block triangular preconditioners were introduced by Shen et al. (2012) for the regularized saddle point problem. However, the spectral analysis of the preconditioner based on the augmentation of the (2,2)(2,2) block was not throughly derived there. In this short paper, we give a detailed spectral analysis on this preconditioner. A numerical example is employed to validate the efficiency of the presented theoretical results.