On eigenvalue distribution of constraint-preconditioned symmetric saddle point matrices

被引：31

作者：

Bergamaschi, Luca ^{[1
]}

机构：

[1] Univ Padua, Dept Math Methods & Models Sci Applicat, I-35121 Padua, Italy

来源：

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS | 2012年 / 19卷 / 04期

关键词：

saddle Point problems; iterative methods; inexact constraint preconditioners; eigenvalues; ITERATIVE SOLUTION; SYSTEMS;

D O I：

10.1002/nla.806

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is devoted to the analysis of the eigenvalue distribution of two classes of block preconditioners for the generalized saddle point problem. Most of the bounds developed improve those appeared in previously published works. Numerical results onto a realistic test problem give evidence of the effectiveness of the estimates on the spectrum of preconditioned matrices. Copyright (c) 2011 John Wiley & Sons, Ltd.

引用

页码：754 / 772

页数：19

共 22 条

[1] Eigenvalue estimates for preconditioned saddle point matrices [J].

Axelsson, O ;

Neytcheva, M .

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 2006, 13 (04) :339-360

[2] Robust approximate inverse preconditioning for the conjugate gradient method [J].

Benzi, M ;

Cullum, JK ;

Tuma, M .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2000, 22 (04) :1318-1332

[3] A comparative study of sparse approximate inverse preconditioners [J].

Benzi, M ;

Tuma, M .

APPLIED NUMERICAL MATHEMATICS, 1999, 30 (2-3) :305-340

[4] On the eigenvalues of a class of saddle point matrices [J].

Benzi, M ;

Simoncini, V .

NUMERISCHE MATHEMATIK, 2006, 103 (02) :173-196

[5]

Benzi M, 2005, ACTA NUMER, V14, P1, DOI 10.1017/S0962492904000212

[6] 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

[7] Mixed Constraint Preconditioners for the iterative solution of FE coupled consolidation equations [J].

Bergamaschi, Luca ;

Ferronato, Massimiliano ;

Gambolati, Giuseppe .

JOURNAL OF COMPUTATIONAL PHYSICS, 2008, 227 (23) :9885-9897

[8] Novel preconditioners for the iterative solution to FE-discretized coupled consolidation equations [J].

Bergamaschi, Luca ;

Ferronato, Massimiliano ;

Gambolati, Giuseppe .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2007, 196 (25-28) :2647-2656

[9] Inexact constraint preconditioners for linear systems arising in interior point methods [J].

Bergamaschi, Luca ;

Gondzio, Jacek ;

Venturin, Manolo ;

Zilli, Giovanni .

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 2007, 36 (2-3) :137-147

[10] General theory of three-dimensional consolidation [J].

Biot, MA .

JOURNAL OF APPLIED PHYSICS, 1941, 12 (02) :155-164

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