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For the system of linear equations arising from discretization of the second-order selfadjoint elliptic Dirichlet-periodic boundary value problems, by making use of the special structure of the coefficient matrix we present a class of combinative preconditioners which are technical combinations of modified incomplete Cholesky factorizations and ShermanMorrison-Woodbury update. Theoretical analyses show that the condition numbers of the preconditioned matrices can be reduced to (h-1), one order smaller than the condition number (h-2) of the original matrix. Numerical implementations show that the resulting preconditioned conjugate gradient methods are feasible, robust and efficient for solving this class of linear systems.