Approximate factorization constraint preconditioners for saddle-point matrices

被引：56

作者：

Dollar, HS ^{[1
]}

Wathen, AJ ^{[1
]}

机构：

[1] Univ Oxford, Comp Lab, Numer Anal Grp, Oxford OX1 3QD, England

来源：

SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2006年 / 27卷 / 05期

关键词：

preconditioning; indefinite linear systems; Krylov subspace methods; conjugate gradient method;

D O I：

10.1137/04060768X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the application of the conjugate gradient method to the solution of large, symmetric indefinite linear systems. Special emphasis is put on the use of constraint preconditioners and a new factorization that can reduce the number of flops required by the preconditioning step. Results concerning the eigenvalues of the preconditioned matrix and its minimum polynomial are given. Numerical experiments validate these conclusions.

引用

页码：1555 / 1572

页数：18

共 14 条

[1] Preconditioning indefinite systems in interior point methods for optimization [J].

Bergamaschi, L ;

Gondzio, J ;

Zilli, G .

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 2004, 28 (02) :149-171

[2]

ELMAN HC, IN PRESS FINITE ELEM

[3]

Fischer B, 1996, Tech. rep.

[4]

Gill P. E., 1981, PRACTICAL OPTIMIZATI

[5]

Golub G. H., 1996, MATRIX COMPUTATIONS

[6] On the solution of equality constrained quadratic programming problems arising in optimization [J].

Gould, NIM ;

Hribar, ME ;

Nocedal, J .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2001, 23 (04) :1375-1394

[7]

GOULD NIM, 2001, TRPA0104 CERFACS

[8] Constraint preconditioning for indefinite linear systems [J].

Keller, C ;

Gould, NIM ;

Wathen, AJ .

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2000, 21 (04) :1300-1317

[9]

Luksan L, 1998, NUMER LINEAR ALGEBR, V5, P219, DOI 10.1002/(SICI)1099-1506(199805/06)5:3<219::AID-NLA134>3.0.CO

[10]

2-7

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