Analysis of Block LDL Factorizations for Symmetric Indefinite Matrices∗
نویسنده
چکیده
We consider the block LDL factorizations for symmetric indefinite matrices in the form LBL , 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 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 factorization using the Bunch-Parlett (complete pivoting), fast Bunch-Parlett or bounded Bunch-Kaufman (rook pivoting) pivoting strategy.
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