Preconditioned Hermitian and skew-Hermitian splitting methods for non-Hemitian positive semidefinite linear systems
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Publication:1882552
DOI10.1007/s00211-004-0521-1zbMath1056.65025OpenAlexW2049726926MaRDI QIDQ1882552
Gene H. Golub, Jianyu Pan, Zhong Zhi Bai
Publication date: 1 October 2004
Published in: Numerische Mathematik (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00211-004-0521-1
convergencenumerical examplespreconditioningnon-Hermitian positive semidefinite linear systemsskew-Hermitian splitting methods
Computational methods for sparse matrices (65F50) Iterative numerical methods for linear systems (65F10) Numerical computation of matrix norms, conditioning, scaling (65F35)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Performance and analysis of saddle point preconditioners for the discrete steady-state Navier-Stokes equations
- Preconditioning by Fast Direct Methods for Nonself-Adjoint Nonseparable Elliptic Equations
- Mixed and Hybrid Finite Element Methods
- Fast Iterative Solution of Stabilised Stokes Systems. Part I: Using Simple Diagonal Preconditioners
- Analysis of the Inexact Uzawa Algorithm for Saddle Point Problems
- An Iteration for Indefinite Systems and Its Application to the Navier--Stokes Equations
- Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive Definite Linear Systems
- A Note on Preconditioning for Indefinite Linear Systems
- On the preconditioning of matrices with skew-symmetric splittings
- Sufficient conditions for the convergent splittings of non-Hermitian positive definite matrices