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The well known block preconditioning technique is modified to suit certain ill-conditioned linear systems arising in reservoir modelling, semiconductor simulation and other fields of applications. Incorporated into the conjugate or biconjugate gradients algorithm, the proposed preconditioner gives a significant improvement in the condition number and the resulting convergence rate.doi:10.1016/0893-9659(91)90173-s fatcat:p4wyxppubzeypbuea67mmw757e