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Symmetric-triangular decomposition and its applications part II: Preconditioners for indefinite systems

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Abstract

As an application of the symmetric-triangular (ST) decomposition given by Golub and Yuan (2001) and Strang (2003), three block ST preconditioners are discussed here for saddle point problems. All three preconditioners transform saddle point problems into a symmetric and positive definite system. The condition number of the three symmetric and positive definite systems are estimated. Therefore, numerical methods for symmetric and positive definite systems can be applied to solve saddle point problems indirectly. A numerical example for the symmetric indefinite system from the finite element approximation to the Stokes equation is given. Finally, some comments are given as well.

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Authors and Affiliations

  1. Department of Mathematics, Hong Kong Baptist University, Kowloon, Hong Kong, China

    Xiaonan Wu

  2. Computer Science Department, Stanford University, Stanford, CA, 94305-9025, USA

    Gene H. Golub

  3. Departamento de Matemática Aplicada e Estátistica, ICMC-São Carlos-USP, Caixa Postal 668, 13.560, São Carlos, SP, Brazil

    José A. Cuminato

  4. Departamento de Matemática – UFPR, Centro Politécnico, CP: 19.081, CEP: 81531-990, Curitiba, Paraná, Brazil

    Jin Yun Yuan

Authors
  1. Xiaonan Wu
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  2. Gene H. Golub
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  3. José A. Cuminato
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  4. Jin Yun Yuan
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Correspondence to Xiaonan Wu.

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65F10

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Wu, X., Golub, G., Cuminato, J. et al. Symmetric-triangular decomposition and its applications part II: Preconditioners for indefinite systems . Bit Numer Math 48, 139–162 (2008). https://doi.org/10.1007/s10543-008-0160-5

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  • DOI: https://doi.org/10.1007/s10543-008-0160-5

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