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- W2022298399 abstract "By using Sherman-Morrison-Woodbury formula, we introduce a preconditioner based on parameterized splitting idea for generalized saddle point problems which may be singular and nonsymmetric. By analyzing the eigenvalues of the preconditioned matrix, we find that when α is big enough, it has an eigenvalue at 1 with multiplicity at least<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M1><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:math>, and the remaining eigenvalues are all located in a unit circle centered at 1. Particularly, when the preconditioner is used in general saddle point problems, it guarantees eigenvalue at 1 with the same multiplicity, and the remaining eigenvalues will tend to 1 as the parameter<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M2><mml:mi>α</mml:mi><mml:mo>→</mml:mo><mml:mn>0</mml:mn></mml:math>. Consequently, this can lead to a good convergence when some GMRES iterative methods are used in Krylov subspace. Numerical results of Stokes problems and Oseen problems are presented to illustrate the behavior of the preconditioner." @default.
- W2022298399 created "2016-06-24" @default.
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- W2022298399 date "2013-01-01" @default.
- W2022298399 modified "2023-10-15" @default.
- W2022298399 title "A Parameterized Splitting Preconditioner for Generalized Saddle Point Problems" @default.
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- W2022298399 doi "https://doi.org/10.1155/2013/489295" @default.
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