New preconditioners for saddle point problems

Applied Mathematics and Computation

Volumn 172, Issue 2 SPEC. ISS., 2006, Pages 762-771

  Pan, Jian Yu ^a   Ng, Michael K ^b   Bai, Zhong Zhi ^c  

^a EAST CHINA NORMAL UNIVERSITY   (China)

^b UNIVERSITY OF HONG KONG   (Hong Kong)

^c INSTITUTE OF COMPUTATIONAL MATHEMATICS AND SCIENTIFIC ENGINEERING COMPUTING   (China)

Author keywords

Eigenvalue distribution; Matrix splitting; Preconditioning; Saddle point problem

Indexed keywords

MATRIX ALGEBRA; PROBLEM SOLVING;

MATRIX SPLITTING; PRECONDITIONING; SADDLE POINT PROBLEM;

EIGENVALUES AND EIGENFUNCTIONS;

EID: 31644446275     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2004.11.016     Document Type: Conference Paper

References (17)

1. Z.-Z. Bai, G.H. Golub, L.-Z. Lu, and J.-F. Yin Block triangular and skew-Hermitian splitting methods for positive definite linear systems SIAM J. Sci. Comput. 2004
2. Z.-Z. Bai, G.H. Golub, and M.K. Ng Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems SIAM J. Matrix Anal. Appl. 24 2003 603 626
3. Z.-Z. Bai, G.H. Golub, and J.-Y. Pan Preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite linear systems Numer. Math. 2004
4. M. Benzi, and G.H. Golub A preconditioner for generalized saddle point problems SIAM J. Matrix Anal. Appl. 2004
5. J.T. Betts Practical Methods for Optimal Control using Nonlinear Programming 2001 SIAM Philadelphia, PA
6. J.H. Bramble, J.E. Pasciak, and A.T. Vassilev Analysis of the inexact Uzawa algorithm for saddle point problems SIAM J. Numer. Anal. 34 1997 1072 1092
7. F. Brezzi, and M. Fortin Mixed and Hybrid Finite Element Methods 1991 Springer-Verlag New York
8. H.C. Elman, and G.H. Golub Inexact and preconditioned Uzawa algorithms for saddle point problems SIAM J. Numer. Anal. 31 1994 1645 1661
9. P.E. Gill, W. Murray, and M.H. Wright Practical Optimization 1981 Academic Press New York
10. R. Glowinski Numerical Methods for Nonlinear Variational Problems 1984 Springer-Verlag New York
11. G.H. Golub, and A.J. Wathen An iteration for indefinite systems and its application to the Navier-Stokes equations SIAM J. Sci. Comput. 19 1998 530 539
12. V. Girault, and P.A. Raviart Finite Element Approximation of the Navier-Stokes Equations 1981 Springer-Verlag New York
13. D. Peaceman, and H. Rachford The numerical solutions of parabolic and elliptic differential equations J. Sco. Indust. Appl. Math. 3 1955 28 41
14. Y. Saad, and M.H. Schultz GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems SIAM J. Sci. Statist. Comput. 7 1986 856 869
15. V. Simoncini, and M. Benzi Spectral properties of the Hermitian and skew-Hermitian splitting preconditioner for saddle point problems SIAM J. Matrix Anal. Appl. 2004
16. G. Strang Introduction to Applied Mathematics 1986 Wellesley-Cambridge Press MA
17. J. Zhao The generalized Cholesky factorization method for saddle point problems Appl. Math. Comput. 92 1998 49 58