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Saddle Point Problem
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Null-Space Preconditioners for Saddle Point Systems,
J. Pestana and T. Rees, SIAM J. Matrix Anal. & Appl., 37 (2016), 1103--1128
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Natural preconditioning and iterative methods for saddle point systems,
J. Pestana and A. J. Wathen, SIAM Review, 2015
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Unified analysis of preconditioning methods for saddle point matrices,
O. Axelsson, NLA, 2015
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On nonsingularity of block two-by-two matrices,
Z. J. Bai and Z. Z. Bai, LAA, 2013.
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Constraint Preconditioners for Symmetric Indefinite Matrices,
Bai, Ng and Wang, SMAX, 2009
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Optimal Parameter in Hermitian and Skew-Hermitian Splitting Method for Certain Two-by-Two Block Matrices,
Bai, Golub and Li, SISC, 2006.
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Block Triangular and Skew-Hermitian Splitting Methods for Positive-Definite Linear Systems,
Bai, Golub, Lu, Yin, SISC, 2005
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On Inexact Preconditioners for Nonsymmetric Matrices,
Bai and Ng, SISC, 2005
- (PPCG)
On the Solution of Equality Constrained Quadratic Programming Problems Arising in Optimization,
N.I.M. Gould, M.E. Hribar and J. Nocedal, SIAM J. Sci. Comput., 23 (2001), 1376-–1395
- (CP)
Constraint Preconditioning for Indefinite Linear System,
C. Keller, N.I.M. Gould and A.J. Wathen, SIAM J. Matrix Anal. Appl., 21 (2000), 1300--1317
HSS and HSS-like
- (HSS)
Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive Definite Linear Systems,
Z.-Z. Bai, G. H. Golub and M. K. Ng, SIAM J. Matrix Anal. & Appl., 24 (2003), 603--626.
- (PHSS)
Preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite linear systems,
Z.-Z. Bai, G. H. Golub and J. Y. Pan, Numerische Mathematik, 98 (2004), 1--32.
- (NSS)
On successive‐overrelaxation acceleration of the Hermitian and skew‐Hermitian splitting iterations,
Z.-Z. Bai, G. H. Golub and M. K. Ng, Numer. Linear Algebra Appl., (14) 2007, 319--335.
- (PSS)
Block Triangular and Skew-Hermitian Splitting Methods for Positive-Definite Linear Systems,
Z.-Z. Bai, G. H. Golub, L. Z. Lu and J. F. Yin, SIAM J. Sci. Comput., 26 (2005), 844--863.
- (PHSS)
Convergence properties of preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite matrices,
Z.-Z. Bai, G. H. Golub and C. K. Li, Mathematics of Computation, 76 (2007), 287--298.
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Several splittings for non-Hermitian linear systems,
Z.-Z. Bai, Science in China Series A: Mathematics, 51 (2008), 1339--1348.
- (GHSS)
A generalized preconditioned HSS method for non-Hermitian positive definite linear systems,
A.-L. Yang, J. An and Y.-J. Wu, Applied Mathematics and Computation, 216 (2010), 1715--1722.
- (GHSS)
Two-parameter generalized Hermitian and skew-Hermitian splitting iteration method,
N. Aghazadeh, D. Khojasteh Salkuyeh & M. Bastani,
International Journal of Computer Mathematics, 93 (2016), 1119--1139.
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On spectral clustering of HSS preconditioner for generalized saddle-point matrices,
Z.-Z. Bai, Linear Algebra and its Applications, 555 (2018), 285--300.
HSS-like for SPP
- (HSS)
A Preconditioner for Generalized Saddle Point Problems,
M. Benzi and G. H. Golub, SIAM J. Matrix Anal. & Appl., 26 (2004), 20--41.
- (HSS)
Spectral Properties of the Hermitian and Skew-Hermitian Splitting Preconditioner for Saddle Point Problems,
V. Simoncini and M. Benzi, SIAM J. Matrix Anal. & Appl., 26 (2004), 377--389.
- (AHSS)
Accelerated Hermitian and skew-Hermitian splitting iteration methods for saddle-point problems,
Z.-Z. Bai and G. H. Golub, IMA Journal of Numerical Analysis, 27 (2007), 1--23.
- (AHSS)
Optimal parameters in the HSS-like methods for saddle-point problems,
Z.-Z. Bai, Numer. Linear Algebra Appl., 16 (2009), 447--479.
Uzawa
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Inexact and Preconditioned Uzawa Algorithms for Saddle Point Problems,
H. C. Elman and G. H. Golub, SIAM J. Numer. Anal., 31 (1994), 1645--1661.
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Analysis of the Inexact Uzawa Algorithm for Saddle Point Problems,
J. H. Bramble, J. E. Pasciak and A. T. Vassilev, SIAM J. Numer. Anal., 34 (1997), 1072--1092
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On the Analysis of Block Smoothers for Saddle Point Problems,
D. Drzisga , L. John, U. Rude, B. Wohlmuth and W. Zulehner, SIAM J. Matrix Anal. & Appl., 39 (2018), 932--960
SOR-like
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SOR-like Methods for Augmented Systems,
G. H. Golub, X. Wu and J.-Y. Yuan, BIT Numerical Mathematics, (41) 2001, 71--85
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On generalized successive overrelaxation methods for augmented linear systems,
Z.-Z. Bai, B. N. Parlett and Z. Q. Wang, Numerische Mathematik, 102 (2005), 1--38
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Modified SOR-like method for the augmented system,
X. Shao, Z. Li and C. Li, International Journal of Computer Mathematics, 84 (2007), 1653--1662
Eddy Current Problem
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