| 数学与计算机科学 |
|
|
|
|
| 解鞍点问题的新SOR类迭代法的一个注记 |
| 张理涛 |
| 郑州航空工业管理学院 理学院, 河南 郑州 450015 |
|
| A note on new SOR-Like method for the saddle point problems |
| ZHANG Litao |
| Department of Mathematics and Physics, Zhengzhou University of Aeronautics, Zhengzhou 450015, China |
[1] WRIGHT S. Stability of augmented system factorizations in interior-point methods[J]. SIAM J Matrix Anal Appl,1997,18:191-222.
[2] ELMAN H , SILVESTER D. Fast nonsymmetric iterations and preconditioning for Navier-Stokes equations[J]. SIAM J Sci Comput,1996,17:33-46.
[3] ELMAN H, GOLUB G H. Inexact and preconditioned Uzawa algorithms for saddle point problems[J]. SIAM J Numer Anal,1994,31:1645-1661.
[4] FISCHER B, RAMAGE A, SILVESTER D J, et al. Minimum residual methods for augmented systems[J]. BIT,1998,38:527-543.
[5] ARIOLI M , DUFF I S , de RIJK P P M. On the augmented system approach to sparse least-squares problems[J]. Numer Math,1989,55:667-684.
[6] SANTOS C H , SILVA B P B , YUAN J Y . Block SOR methods for rank deficient least squares problems[J]. J Comput Appl Math,1998,100:1-9.
[7] YUAN J Y. Numerical methods for generalized least squares problems[J]. J Comput Appl Math,1996,66:571-584.
[8] YUAN J Y, IUSEM A N . Preconditioned conjugate gradient method for generalized least squares problems[J]. J Comput Appl Math,1996,71:287-297.
[9] GOLUB H , WU X, YUAN J Y.SOR-like methods for augmented systems[J]. BIT,2001,41:71-85.
[10] DARVISHIM T ,HESSARI P . Symmetric SOR method for augmented systems[J]. Appl Math Comput,2006,183:409-415.
[11] BAI Z Z, PARLETT B N, WANG Z Q. On generalized successive overrelaxation methods for augmented linear systems[J]. Numer Math,2005,102:1-38.
[12] BAI Z Z, WANG Z Q. On parameterized inexact Uzawa methods for generalized saddle point problems[J]. Linear Algebra Appl,2008,428:2900-2932.
[13] CHEN F, JIANG Y L. A generalization of the inexact parameterized Uzawa methods for saddle point problems[J]. Appl Math Comput,2008,206:765-771.
[14] ZHENG B, BAI Z Z, YANG X. On semi-convergence of parameterized Uzawa methods for singular saddle point problems[J]. Linear Algebra Appl,2009,431:808-817.
[15] ZHANG G F , LU Q H. On generalized symmetric SOR method for augmented systems[J]. J Comput Appl Math,2008,1(15):51-58.
[16] PENG X F , LI W . On unsymmetric block overrelaxation-type methods for saddle point[J]. Appl Math Comput,2008,203(2):660-671.
[17] BAI Z Z, YANG X . On HSS-based iteration methods for weakly nonlinear systems[J]. Appl Numer Math,2009,59:2923-2936.
[18] BAI Z Z, GOLUB G H, MICHAEL K N .On inexact hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems[J]. Linear Algebra Appl,2008,428:413-440.
[19] BAI Z Z. Several splittings for non-Hermitian linear systems[J]. Science in China, Ser A: Math,2008,51:1339-1348.
[20] BAIZ Z, GOLUB G H,LU L Z , et al. Block-Triangular and skew-Hermitian splitting methods for positive definite linear systems[J].SIAM J Sci Comput,2005,26:844-863.
[21] BAI Z Z, GOLUB G H, NG M K. Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems[J]. SIAM J Matrix Anal A,2003,24:603-626.
[22] WANG L , BAI Z Z . Convergence conditions for splitting iteration methods for non-Hermitian linear systems[J]. Linear Algebra Appl,2008,428:453-468.
[23] WU S L , HUANG T Z , ZHAO X L. A modified SSOR iterative method for augmented systems[J]. J Comput Appl Math,2009,228(1):424-433.
[24] ZHANG L T,HUANG T Z,CHENG S H, et al. Convergence of a generalized MSSOR method for augmented systems[J]. J Comput Appl Math,2012,236:1841-1850.
[25] ZHANG L T. A new preconditioner for generalized saddle matrices with highly singular(1,1) blocks[J].Int J Comput Math, 2014, 91(9):2091-2101.
[26] MIAO S X , WANG K . On generalized stationary iterative method for solving the saddle point problems[J].J Appl Math Comput,2011,35:459-468.
[27] ZHENG Q Q, MA C F. A new SOR-Like method for the saddle point problems[J]. Appl Math Comput,2014,233:421-429.
[28] SHAO X, SHEN H, LI C. The generalized SOR-Like method for the augmented systems[J]. Int J Inf Syst Sci,2006(2):92-98.
[29] |
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
| |
Shared |
|
|
|
|
| |
Discussed |
|
|
|
|
