Approximate factorization constraint preconditioners for saddle-point matrices

SIAM Journal on Scientific Computing

Volumn 27, Issue 5, 2006, Pages 1555-1572

  Dollar, H S ^a   Wathen, A J ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

Conjugate gradient method; Indefinite linear systems; Krylov subspace methods; Preconditioning

Indexed keywords

CONSTRAINT THEORY; MATRIX ALGEBRA; NATURAL SCIENCES COMPUTING; NUMERICAL ANALYSIS; POLYNOMIAL APPROXIMATION;

CONJUGATE GRADIENT METHODS; INDEFINITE LINEAR SYSTEMS; KRYLOV SUBSPACE METHODS; PRECONDITIONING;

LINEAR SYSTEMS;

EID: 33748759589     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/04060768X     Document Type: Conference Paper

References (13)

1. L. BERGAMASCHI, J. GONDZIO, AND G. ZILLI, Preconditioning indefinite systems in interior point methods for optimization, Comput. Optim. Appl., 28 (2004), pp. 149-171.
2. H. C. ELMAN, D. J. SILVESTER, AND A. J. WATHEN, Finite Elements and Fast Iterative Solvers: With Applications in Incompressible Fluid Dynamics, Oxford University Press, Oxford, UK, to appear.
3. B. FISCHER, Polynomial Based Iteration Methods for Symmetric Linear Systems, Adv. Numer. Math., John Wiley & Sons Ltd., Chichester, UK; B. G. Teubner, Stuttgart, Germany, 1996.
4. P. E. GILL, W. MURRAY, AND M. H. WRIGHT, Practical Optimization, Academic Press Inc. [Harcourt Brace Jovanovich Publishers], London, 1981.
5. G. H. GOLUB AND C. F. VAN LOAN, Matrix Computations, 3rd ed., Johns Hopkins Stud. Math. Sci., Johns Hopkins University Press, Baltimore, MD, 1996.
6. N. I. M. GOULD, D. ORBAN, AND PH. L. TOINT, CUTEr (and SifDec), a Constrained and Unconstrained Testing Environment, Revisited, Tech. Report TR/PA/01/04, CERFACS, Toulouse, France, 2001.
7. N. I. M. GOULD, M. E. HRIBAR, AND J. NOCEDAL, On the solution of equality constrained quadratic programming problems arising in optimization, SIAM J. Sci. Comput., 23 (2001), pp. 1376-1395.
8. C. KELLER, N. I. M. GOULD, AND A. J. WATHEN, Constraint preconditioning for indefinite linear systems, SIAM J. Matrix Anal. Appl., 21 (2000), pp. 1300-1317.
9. L. LUKŠAN AND J. VLČEK, Indefinitely preconditioned inexact Newton method for large sparse equality constrained non-linear programming problems, Numer. Linear Algebra Appl., 5 (1998), pp. 219-247.
10. A. QUARTERONI AND A. VALLI, Numerical Approximation of Partial Differential Equations, Springer Series in Computational Mathematics 23, Springer-Verlag, Berlin, 1994.
11. W. SCHILDERS, private communication, 2002.
12. H. A. VAN DER VORST, Iterative Krylov Methods for Large Linear Systems, Cambridge Monographs on Applied and Computationl Mathematics, Cambridge University Press, Cambridge, UK, 2003.
13. S. J. WRIGHT, Primal-Dual Interior-Point Methods, SIAM, Philadelphia, PA, 1997.