[1]
|
K. J. Arrow, L. Hurwicz, H. Uzawa, Studies in Linear and Nonlinear Programming, Stanford University Press, Stanford, 1958.
Google Scholar
|
[2]
|
Z. J. Bai, Z. Z. Bai, On nonsingularity of block two-by-two matrices, Linear Algebra Appl., 2013, 439, 2388-2404. doi: 10.1016/j.laa.2013.06.004
CrossRef Google Scholar
|
[3]
|
Z. Z. Bai, G. H. Golub, M. K. Ng, Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems, SIAM J. Matrix Anal. Appl., 2003, 24, 603-626. doi: 10.1137/S0895479801395458
CrossRef Google Scholar
|
[4]
|
Z. Z. Bai, B. N. Parlett, Z. Q. Wang, On generalized successive overrelaxation methods for augmented linear systems, Numer. Math., 2005, 102, 1-38. doi: 10.1007/s00211-005-0643-0
CrossRef Google Scholar
|
[5]
|
Z. Z. Bai, J. F. Yin, Y. F. Su, A shift-splitting preconditioner for non-Hermitian positive definite matrices, J. Comput. Math., 2006, 24, 539-552.
Google Scholar
|
[6]
|
M. Benzi, G. H. Golub, J. Liesen, Numerical solution of saddle point problems, Acta. Numer., 2005, 14, 1-137. doi: 10.1017/S0962492904000212
CrossRef Google Scholar
|
[7]
|
A. Berman, R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, SIAM, Philadelphia, PA, 1994.
Google Scholar
|
[8]
|
D. Bertaccini, G. H. Golub, S. S. Capizzano, C. T. Possio, Preconditioned HSS methods for the solution of non-Hermitian positive definite linear systems and applications to the discrete convection-diffusion equation, Numer. Math., 2005, 99, 441-484. doi: 10.1007/s00211-004-0574-1
CrossRef Google Scholar
|
[9]
|
Y. Cao, M. Q. Jiang, Y. L. Zheng, A splitting preconditioner for saddle point problems, Numer. Linear Algebra Appl., 2011, 18, 875-895. doi: 10.1002/nla.772
CrossRef Google Scholar
|
[10]
|
Y. Cao, S. C. Yi, A class of Uzawa-PSS iteration methods for nonsingular and singular non-Hermitian saddle point problems, Appl. Math. Comput., 2016, 275, 41-49.
Google Scholar
|
[11]
|
Z. Chao, G. Cheng, Semi-convergence analysis of the Uzawa-SOR methods for singular saddle point problems, Appl. Math. Letters, 2014, 35, 52-57. doi: 10.1016/j.aml.2014.04.014
CrossRef Google Scholar
|
[12]
|
Y. Dou, A.-L. Yang, Y. J. Wu, A new Uzawa-type iteration method for non-Hermitian saddle-point problems, East J. Appl. Math., 2017, 7, 211-226. doi: 10.4208/eajam.290816.130117a
CrossRef Google Scholar
|
[13]
|
G. H. Golub, X. Wu, J. Y. Yuan, SOR-like methods for augmented systems, BIT Numer. Math., 2001, 41, 71-85. doi: 10.1023/A:1021965717530
CrossRef Google Scholar
|
[14]
|
Z. G. Huang, L. G. Wang, Z. Xu, J. J. Cui, The generalized Uzawa-SHSS method for non-Hermitian saddle-point problems, Comput. Appl. Math., 2018, 37, 1213-1231. doi: 10.1007/s40314-016-0390-0
CrossRef Google Scholar
|
[15]
|
M. Q. Jiang, Y. Cao, On local Hermitian and skew-Hermitian splitting iteration methods for generalized saddle point problems, J. Comput. Appl. Math., 2009, 231, 973-982. doi: 10.1016/j.cam.2009.05.012
CrossRef Google Scholar
|
[16]
|
C. X. Li, S. L. Wu, A single-step HSS method for non-Hermitian positive definite linear systems, Appl. Math. Lett., 2015, 44, 26-29. doi: 10.1016/j.aml.2014.12.013
CrossRef Google Scholar
|
[17]
|
Z. Li, M. C. Lai, X. Peng, Z. Zhang, A least squares augmented immersed interface method for solving Navier-Stokes and Darcy coupling equations, Computers and Fluids, 2018, 167, 384-399. doi: 10.1016/j.compfluid.2018.03.032
CrossRef Google Scholar
|
[18]
|
S. X. Miao, A new Uzawa-type method for saddle point problems, Appl. Math. Comput., 2017, 300, 95-102.
Google Scholar
|
[19]
|
J. J. H. Miller, On the location of zeros of certain classes of polynomials with applications to numerical analysis, J. Inst. Math. Appl., 1971, 8, 397-406. doi: 10.1093/imamat/8.3.397
CrossRef Google Scholar
|
[20]
|
X. Wu, B. P. B. Silva, J. Y. Yuan, Conjugate gradient method for rank deficient saddle point problem, Numer. Algor., 2004, 35, 139-154. doi: 10.1023/B:NUMA.0000021758.65113.f5
CrossRef Google Scholar
|
[21]
|
J. S. Xiong, X. B. Gao, Semi-convergence analysis of Uzawa-AOR method for singular saddle point problems, Comp. Appl. Math., 2017, 36, 383-395. doi: 10.1007/s40314-015-0233-4
CrossRef Google Scholar
|
[22]
|
A. L. Yang, X. Li, Y. J. Wu, On semi-convergence of the Uzawa-HSS method for singular saddle-point problems, Appl. Math. Comput., 2015, 252, 88-98.
Google Scholar
|
[23]
|
A. L. Yang, Y. J. Wu, The Uzawa-HSS method for saddle-point problems, Appl. Math. Lett., 2014, 38, 38-42. doi: 10.1016/j.aml.2014.06.018
CrossRef Google Scholar
|
[24]
|
J. Y. Yuan, Numerical methods for generalized least squares problem, J. Comput.Appl. Math., 1996, 66, 571-584. doi: 10.1016/0377-0427(95)00167-0
CrossRef Google Scholar
|
[25]
|
J. H. Yun, Variants of the Uzawa method for saddle point problem, Comput. Math. Appl., 2013, 65, 1037-1046. doi: 10.1016/j.camwa.2013.01.037
CrossRef Google Scholar
|
[26]
|
J. J. Zhang, J. J. Shang, A class of Uzawa-SOR methods for saddle point problems, Appl. Math. Comput., 2010, 216, 2163-2168.
Google Scholar
|
[27]
|
N. M. Zhang, T. T. Lu, Y. M. Wei, Semi-convergence analysis of Uzawa methods for singular saddle point problems, J. Comput. Appl. Math., 2014, 255, 334-345. doi: 10.1016/j.cam.2013.05.015
CrossRef Google Scholar
|
[28]
|
N. M. Zhang, Y. M. Wei, On the convergence of general stationary iterative methods for Range- Hermitian singular linear systems, Numer. Linear Algebra Appl., 2010, 17, 139-154. doi: 10.1002/nla.663
CrossRef Google Scholar
|
[29]
|
B. Zheng, Z. Z. Bai, X. Yang, On semi-convergence of parameterized Uzawa methods for singular saddle point problems, Linear Algebra Appl., 2009, 431, 808-817. doi: 10.1016/j.laa.2009.03.033
CrossRef Google Scholar
|