数学与计算机科学 |
|
|
|
|
解非对称鞍点问题的广义交替分裂预处理子的一个注记 |
张理涛1, 谷同祥2, 孟慧丽3 |
1. 郑州航空工业管理学院 理学院, 河南 郑州 450015; 2. 北京应用物理与计算数学研究所 计算物理实验室, 北京 100088; 3. 河南师范大学 计算机与信息工程学院, 河南 新乡 453007 |
|
A note of generalized shift-splitting preconditioners for nonsymmetric saddle point problems |
ZHANG Litao1, GU Tongxiang2, MENG Huili3 |
1. College of Science, Zhengzhou University of Aeronautics, Zhengzhou 450015, China; 2. Laboratory of Computationary Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China; 3. College of Computer and Information Engineering, Henan Normal University, Xinxiang 453007, Henan Province, 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 Y F. 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 G H, WU X, YUAN J Y. SOR-like methods for augmented systems[J]. BIT,2001,55:71-85. [10] DARVISHI M 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] BAI Z 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] JIANG M Q, CAO Y. On local Hermitian skew-Hermitian splitting iteration methods for generalized saddle point problems[J]. J Comput Appl Math,2009,231:973-982. [23] WANG L, BAI Z Z. Convergence conditions for splitting iteration methods for non-Hermitian linear systems[J]. Linear Algebra Appl,2008,428:453-468. [24] 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. [25] BAI Z Z, ZHANG S L. A regularized conjugate gradient method for symmetric positive definite system of linear equations[J]. J Comput Math,2002,20:437-448. [26] BAI Z Z, YIN J F, SU Y F. A shift-splitting preconditioner for non-Hermitian positive definite matrices[J]. J Comput Math,2006,24:539-552. [27] CAO Y, DU J, NIU Q. Shift-splitting preconditioners for saddle point problems[J]. J Comput Appl Math,2014,272:239-250. [28] CHEN C R, MA C F. A generalized shift-splitting preconditioner for saddle point problems[J]. Appl Math Let |
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
|
Shared |
|
|
|
|
|
Discussed |
|
|
|
|