Perturbation analysis of generalized saddle point systems

Linear Algebra and Its Applications

Volumn 419, Issue 1, 2006, Pages 8-23

  Xiang, Hua ^a   Wei, Yimin ^b   Diao, Huaian ^c  

^a WUHAN UNIVERSITY   (China)

^b FUDAN UNIVERSITY   (China)

^c CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Condition number; KKT; Perturbation analysis; Saddle point systems

Indexed keywords

BOUNDARY CONDITIONS; COMPUTABILITY AND DECIDABILITY; LINEAR ALGEBRA; PROBLEM SOLVING;

CONDITION NUMBER; SADDLE POINT SYSTEMS;

PERTURBATION TECHNIQUES;

EID: 33748299585     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2006.03.041     Document Type: Article

References (27)

1. Amara M., Chacon Vera E., and Trujillo D. Vorticity-velocity-pressure formulation for Stokes problem. Math. Comput. 73 (2003) 1673-1697
2. Benzi M., Golub G.H., and Liesen J. Numerical solution of saddle point problems. Acta Numer. 14 (2005) 1-137
3. Bochev P., and Lehoucq R.B. On the finite element solution of the pure Neumann problem. SIAM Rev. 47 (2005) 50-66
4. Brown P.N., and Walker H.F. GMRES on (nearly) singular systems. SIAM J. Matrix Anal. Appl. 18 (1997) 37-51
5. Cao Z. Comparison of performance of iterative methods for singular and nonsingular saddle point linear systems arising from Navier-Stokes equations. Appl. Math. Comput. 174 (2006) 630-642
6. Chen K. Matrix Preconditioning Techniques and Applications (2005), Cambridge University Press
7. Drkosova J., Greenbaum A., Rozloznik M., and Strakos Z. Numerical stability of GMRES. BIT 35 (1995) 309-330
8. Elman H., Silvester D.J., and Wathen A. Finite Elements and Fast Iterative Solver: with Applications in Incompressible Fluid Dynamics (2005), Oxford University Press
9. Fortin M. Finite element solution of the Navier-Stokes equations. Acta Numer. (1993) 239-284
10. Gohberg I., and Koltracht I. On the inversion of Cauchy matrices. Proceedings of the International Symposium MTNS-89 vol. III (1990), Birkhauser 38-392
11. Gohberg I., and Koltracht I. Mixed, componentwise, and structured condition numbers. SIAM J. Matrix Anal. Appl. 14 (1993) 688-704
12. Gresho P.M., and Sani R.L. Incompressible Flow and the Finite Element Method. Isothermal Laminar Flow vol. 2 (1998), John Wiley & Sons Ltd.
13. Gulliksson M., and Wedin P. Perturbation theory for generalized and constrained linear least squares. Numer. Linear Algebra Appl. 7 (2000) 181-195
14. Gulliksson M., Jin X., and Wei Y. Perturbation bounds for constrained and weighted least squares problems. Linear Algebra Appl. 349 (2002) 221-232
15. Hall F.J. Generalized inverses of a bordered matrix of operators. SIAM J. Appl. Math. 1 (1975) 152-163
16. Higham N.J. Accuracy and Stability of Numerical Algorithms. second ed. (2002), SIAM
17. Kenney C.S., Laub A.J., and Reese M.S. Statistical condition estimation for linear systems. SIAM J. Sci. Comput. 19 (1998) 566-583
18. Konstantinov M., Gu D., Mehrmann V., and Petkov P. Perturbation Theory for Matrix Equations (2003), Elsevier
19. Li X., and Liu X. Structured backward errors for structured KKT systems. J. Comp. Math. 22 (2004) 605-610
20. Nocedal J., and Wright S. Numerical Optimization (1999), Springer-Verlag, New York
21. Paige C.C., Rozloznik M., and Strakos Z. Modified Gram-Schmidt (MGS), least squares, and backward stability of MGS-GMRES. SIAM J. Matrix Anal. Appl. 28 (2006) 264-284
22. Strang G. A framework for equilibrium equations. SIAM Rev. 30 (1988) 283-297
23. Sun J. Structured backward errors for KKT systems. Linear Algebra Appl. 288 (1999) 75-88
24. Vavasis S.A. Stable numerical algorithms for equilibrium systems. SIAM J. Matrix Anal. Appl. 15 (1994) 1108-1131
25. Wang G., Wei Y., and Qiao S. Generalized Inverse: Theory and Computations (2004), Science Press, Beijing/New York
26. Zhang N., and Wei Y. Solving EP singular linear systems. Int. J. Comput. Math. 81 (2004) 1395-1405
27. Zhang N., and Wei Y. A note on solving EP inconsistent linear systems. Appl. Math. Comput. 169 (2005) 8-15