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Type: Text × Subject: Schur complement ×

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Now showing 1 - 3 of 3
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    A multilevel Schur complement preconditioner with ILU factorization for complex symmetric matrices
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Schlundt, Rainer
    This paper describes a multilevel preconditioning technique for solving complex symmetric sparse linear systems. The coefficient matrix is first decoupled by domain decomposition and then an approximate inverse of the original matrix is computed level by level. This approximate inverse is based on low rank approximations of the local Schur complements. For this, a symmetric singular value decomposition of a complex symmetric matix is used. The block-diagonal matrices are decomposed by an incomplete LDLT factorization with the Bunch-Kaufman pivoting method. Using the example of Maxwells equations the generality of the approach is demonstrated.
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    A multilevel Schur complement preconditioner for complex symmetric matrices
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Schlundt, Rainer
    This paper describes a multilevel preconditioning technique for solving complex symmetric sparse linear systems. The coefficient matrix is first decoupled by domain decomposition and then an approximate inverse of the original matrix is computed level by level. This approximate inverse is based on low rank approximations of the local Schur complements. For this, a symmetric singular value decomposition of a complex symmetric matix is used. Using the example of Maxwells equations the generality of the approach is demonstrated.
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    Preconditioning of block tridiagonal matrices
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2008) Axelsson, Owe; Karátson, János
    Preconditioning methods via approximate block factorization for block tridiagonal matrices are studied. Bounds for the resulting condition numbers are given, and two methods for the recursive construction of the approximate Schur complements are presented. Illustrations for elliptic problems are also given, including a study of sensitivity to jumps in the coefficients and of a suitably motidied Poincaré-Steklov operator on the continuous level.