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Volume 9, Number 3, 2019, Pages 916-927                                                                DOI:10.11948/2156-907X.20180168
A note on block preconditioner for generalized saddle point matrices with highly singular (1,1) block
Litao Zhang,Yongwei Zhou,Xianyu Zuo,Chaoqian Li,Yaotang Li
Keywords:Saddle point matrices, Krylov subspace methods, generalized saddle point matrices, minimal polynomial, preconditioners.
      In this paper, we present a block triangular preconditioner for generalized saddle point matrices whose coefficient matrices have singular (1,1) blocks. Theoretical analysis shows that all the eigenvalues of the preconditioned matrix are strongly clustered when choosing an optimal parameter. Numerical experiments are given to demonstrate the efficiency of the presented preconditioner.
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