Note on preconditioning for indefinite linear systems

SIAM Journal on Scientific Computing

Volumn 21, Issue 6, 2000, Pages 1969-1972

  Murphy, Malcolm F ^a   Golub, Gene H ^c   Wathen, Andrew J ^b  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

^b UNIVERSITY OF OXFORD   (United Kingdom)

^c NONE

Author keywords

[No Author keywords available]

Indexed keywords

INDEFINITE LINEAR SYSTEMS; KRYLOV SUBSPACE ITERATIVE METHOD; PRECONDITIONING; SCHUR COMPLEMENT;

APPROXIMATION THEORY; EIGENVALUES AND EIGENFUNCTIONS; GALERKIN METHODS; ITERATIVE METHODS; LINEAR SYSTEMS; MATRIX ALGEBRA; POLYNOMIALS; THEOREM PROVING;

NATURAL SCIENCES COMPUTING;

EID: 0034497397     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827599355153     Document Type: Article

References (13)

1. F. BREZZI, New applications of mixed finite element methods, in Proceedings of the International Congress of Mathematicians 1986, A.M. Gleason, ed., AMS, Providence, RI, 1987, pp. 1335-1347.
2. P.T. BOGGS AND J.W. TOLLE, Sequential quadratic programming, Acta Numerica, Cambridge University Press, Cambridge, UK. 1995, pp. 1-51.
3. H. ELMAN AND D. SILVESTER, Fast nonsymmetric iterations and preconditioning for Navier-Stokes equations, SIAM J. Sci. Comput., 17 (1996), pp. 33-46.
4. H.C. ELMAN, D.J. SILVESTER, AND A.J. WATHEN, Iterative methods for problems in Computational Fluid Dynamics, in Iterative Methods in Scientific Computing, R.H. Chan, T.F. Chan, and G.H. Golub, eds., Springer-Verlag, Singapore, 1997. pp. 271-327.
5. H.C. ELMAN AND G.H. GOLUB, Inexact and preconditioned Uzawa algorithms for saddle point problems, SIAM J. Numer. Anal., 31 (1994), pp. 1645-1661.
6. R. FREUND, G.H. GOLUB, AND N. NACHTIGAL, Iterative solution of linear systems, Acta Numerica, Cambridge University Press, Cambridge, UK, 1992, pp. 57-100.
7. P.E. GILL, W. MURRAY, D.B. PONCELEÓN, AND M.A. SAUNDERS, Preconditioners for indefinite systems arising in optimization, SIAM J. Matrix Anal. Appl., 13 (1992), pp. 292-311.
8. L. HEMMINGSSON AND A.J. WATHEN, A Nearly Optimal Preconditioner for the Navier-Stokes Equations, Oxford University Computing Laboratory, Numerical Analysis report 99/15; Numer. Linear Algebra Appl., 1999, submitted.
9. J. MARYŠKA, M. ROZLOŽNÍK, AND M. TUMA, The potential fluid flow problem and the convergence rate of the minimum residual method, Numer. Linear Alg. Appl., 3 (1996), pp. 525-542.
10. C.C. PAIGE AND M.A. SAUNDERS, Solution of sparse indefinite systems of linear equations, SIAM J. Numer. Anal., 12 (1975), pp. 617-629.
11. I. PERUGIA, V. SIMONCINI, AND M. ARIOLI, Linear algebra methods in a mixed approximation of magnetostatics problems, SIAM J. Sci. Comput., 21 (1999), pp. 1085-1101.
12. Y. SAAD AND M. SCHULTZ, GMRES: A generalized minimum residual algorithm for solving nonsymmetric linear systems, SIAM J. Sci. Statist. Comput., 7 (1986), pp. 856-869.
13. D.J. SILVESTER AND A.J. WATHEN, Fast iterative solution of stabilized Stokes systems Part II: Using general block preconditioners, SIAM J. Numer. Anal., 31 (1994), pp. 1352-1367.