Augmentation Block Triangular Preconditioners for Regularized Saddle Point Problems

Abstract

For regularized saddle point problems, we present two block triangular preconditioners, which can be applied to the saddle point problems with singular or ill-conditioned (1,1) blocks. One is based on the augmentation of the (1,1) block, and the other is based on the augmentation of the (2,2) block. When some special weighted matrices are chosen, the degree of the minimal polynomial of the preconditioned saddle point matrix is $2$. The spectral properties of the presented preconditioners are studied in detail. Numerical experiments demonstrate the performance of the new preconditioners.