鞍点问题的广义位移分裂预条件子

GENERALIZED SHIFT SPLITTING PRECONDITIONERS FOR SADDLE POINT PROBLEMS

对于大型稀疏非Hermitian正定线性方程组,Bai等人提出了一种位移分裂预条件子(J.Comput.Math.,24(2006)539-552).本文将这种思想用到鞍点问题上并提出了一种广义位移分裂(Generalized Shift Splitting,GSS)预条件子,同时证明了该预条件子所对应分裂迭代法的无条件收敛性.最后用数值算例验证了新预条件子的有效性.

For large and sparse non-Hermitian positive definite linear systems, Bai et al. proposed a shift splitting preconditioner （J. Comput. Math., 24 （2006） 539-552）. In this papere we extend this idea to study saddle point problems and present a generalized shift splitting preconditioner. The unconditional convergent property of the corresponding iterative method is proved. Finally, some numerical experiments are illustrated to show the efficiency of the new preconditioners.