An algebraic analysis of a block diagonal preconditioner for saddle point systems

被引：23

作者：

Golub, GH

Greif, C

Varah, JM

机构：

[1] Stanford Univ, SCCM Program, Stanford, CA 94305 USA

[2] Univ British Columbia, Dept Comp Sci, Vancouver, BC V6T 1Z4, Canada

来源：

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 2005年 / 27卷 / 03期

关键词：

saddle point linear systems; augmented Lagrangian; block preconditioning; positive semidefinite matrix; null space;

D O I：

10.1137/04060679X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a positive definite block preconditioner for solving saddle point linear systems. An approach based on augmenting the (1,1) block while keeping its condition number small is described, and algebraic analysis is performed. Ways of selecting the parameters involved are discussed, and analytical and numerical observations are given.

引用

页码：779 / 792

页数：14

共 50 条

[21] Analysis of the relaxed deteriorated PSS preconditioner for singular saddle point linear systems
Liang, Zhao-Zheng
Zhang, Guo-Feng
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2017, 305 : 308 - 322
[22] Using partial spectral information for block diagonal preconditioning of saddle-point systems
Ramage, Alison
Ruiz, Daniel
Sartenaer, Annick
Tannier, Charlotte
[J]. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 2021, 78 (02) : 353 - 375
[23] Eigenvalue estimates of an indefinite block triangular preconditioner for saddle point problems
Wu, Shi-Liang
Li, Cui-Xia
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2014, 260 : 349 - 355
[24] A modified preconditioner for three-by-three block saddle point problems
Li, Jun
Li, Zhenping
[J]. JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS, 2024, 41 (01) : 659 - 680
[25] A modified preconditioner for three-by-three block saddle point problems
Jun Li
Zhenping Li
[J]. Japan Journal of Industrial and Applied Mathematics, 2024, 41 : 659 - 680
[26] A block triangular preconditioner for a class of three-by-three block saddle point problems
Hamed Aslani
Davod Khojasteh Salkuyeh
[J]. Japan Journal of Industrial and Applied Mathematics, 2023, 40 : 1015 - 1030
[27] A block triangular preconditioner for a class of three-by-three block saddle point problems
Aslani, Hamed
Salkuyeh, Davod Khojasteh
[J]. JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS, 2023, 40 (02) : 1015 - 1030
[28] A New Block Preconditioner for Double Saddle Point Systems Arising from Liquid Crystal Directors Modeling
Zhang, Jian-Jun
Liu, Jia-Qi
[J]. COMMUNICATIONS ON APPLIED MATHEMATICS AND COMPUTATION, 2024,
[29] On preconditioner updates for sequences of saddle-point linear systems
De Simone, Valentian
di Serafino, Daniela
Morini, Benedetta
[J]. COMMUNICATIONS IN APPLIED AND INDUSTRIAL MATHEMATICS, 2018, 9 (01): : 35 - 41
[30] A block upper triangular preconditioner with two parameters for saddle-point problems
Xiao, Xiao-Yong
Wang, Cha-Sheng
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2024, 160 : 15 - 29

← 1 2 3 4 5 →