We consider the block LDL^T factorizations for symmetric indefinite matrices in the form LBL^T, where L is unit lower triangular and B is block diagonal with each diagonal block having dimension 1 or 2. The stability of this factorization and its application to solving linear systems has been well-studied in the literature. In this paper we give a condition under which the LBL T factorization will run to completion in inexact arithmetic with inertia preserved. We also analyze the stability of rank estimation for symmetric indefinite matrices by LBL^T factorization using the Bunch-Parlett (complete pivoting), fast Bunch-Parlett or bounded Bunch-Kaufman (rook pivoting) pivoting strategy
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