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 A note on block preconditioner for generalized saddle point matrices with highly singular(1,1) block Li-Tao Zhang 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.