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 Volume 9, Number 3, 2019, Pages 916-927 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. Abstract: 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. PDF      Download reader