On IOM(q): The incomplete orthogonalization method for large unsymmetric linear systems

Numerical Linear Algebra with Applications

Volumn 3, Issue 6, 1996, Pages 491-512

  Jia, Zhongxiao ^a  

^a DALIAN UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Basis vector; Convergence; FOM; IOM(q); Krylov subspace; Orthonormality; Restarted; Truncated; Unsymmetric

Indexed keywords

EID: 21444439486     PISSN: 10705325     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1099-1506(199611/12)3:6<491::AID-NLA87>3.0.CO;2-9     Document Type: Article

References (24)

1. A. E. Arnoldi. The principle of minimized iteration in the solution of the matrix eigenvalue problem. Quart. Appl. Math., 9, 11-29, 1951.
2. O. Axelsson. On preconditioned conjugate gradient methods, CNA-143, Center for Numerical Analysis, University of Texas, Austin, 1978.
3. O. Axelsson. Conjugate gradient type methods for unsymmetric and inconsistent systems of linear equations. Linear Algebra Appl., 29, 1-16, 1980.
4. O. Axelsson. A generalized conjugate gradient direction method and its application on a singular perturbation problem. In G. A. Watson, editor, Proceedings of the 8th Biennial Numerical Analysis Conference, Lecture Notes in Mathematics, Springer-Verlag, No. 773, pages 1-1, 1980.
5. R. Barrett, M. Berry, T. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine and H. A. Van der Vorst. Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, SIAM, Philadephia, 1993.
6. P. N. Brown and A. C. Hindmarsh. Reduced storage methods in stiff ODE systems. Appl. Math. Comput., 31, 40-91, 1989.
7. P. N. Brown and Y. Saad. Hybrid Krylov methods for nonlinear systems of equations. SIAM J. Sci. Stat. Comput., 11, 450-481, 1990.
8. P. N. Brown. A theoretical comparison of the Arnoldi and GMRES algorithms. SIAM J. Sci. Stat. Comput., 12, 58-78, 1991.
9. A. Chronopoulos. s-step iterative methods for (non)symmetric (in)definite linear systems. SIAM J. Numer. Anal., 28, 1776-1789, 1991.
10. A. Chronopoulos. Krylov subspace iterative methods for nonsymmetric indefinite linear systems. Tech. Rep. 90-21, Computer Science Dept., University of Minnesota, 1990.
11. S. C. Eisenstat, H. C. Elman and M. H. Schultz. Variational iterative methods for nonsymmetric systems of linear equations. SIAM J. Numer. Anal., 20, 345-357, 1983.
12. H. C. Elman. Iterative methods for large sparse nonsymmetric systems of linear equations. Ph.D. Thesis, Computer Science Dept., Yale University, 1982.
13. V. Faber and T. Manteuffel. Necessary and sufficient conditions for the existence of a conjugate gradient method. SIAM J. Numer. Anal., 21, 352-362, 1984.
14. V. Faber and T. Manteuffel. Orthogonal error methods. SIAM J. Numer. Anal., 24, 170-187, 1987.
15. R. Fletcher. Conjugate gradient methods for indefinite systems. In G. A. Watson, editor, Proceedings of the 6th Numerical Analysis Conference, Lecture Notes in Mathematics, Springer-Verlag, No. 506, pages 73-89, 1976.
16. R. W. Freund and N. M. Nachtigal. QMR: a quasi-minimal residual method for non-Hermitian linear systems. Numer. Math., 60, 291-313, 1991.
17. R. W. Freund, G. H. Golub and N. M. Nachtigal. Iterative solution of linear systems. Acta. Numerica, 1-44, 1992.
18. G. W. Gear and Y. Saad. Iterative solution of linear equations in ODE codes. SIAM J. Sci. Stat. Comput., 4, 583-601, 1983.
19. G. H. Golub and C. F. Van Loan. Matrix Computations, 2nd Edition, the Hopkins University Press, Baltimore, 1989.
20. G. H. Golub and D. P. O'Leary. Some history of the conjugate gradient and Lanczos algorithms: 1946-1976. SIAM Review, 31, 50-102, 1989.
21. J. F. Grcar. Operator coefficient methods for linear equations. Tech. Rep. Sand89-8691, Sandia National Laboratories, 1989.
22. A. Greenbaum and Z. Strakos. Matrices that generate the same Krylov residual spaces. In G. Golub, A. Greenbaum and M. Luskin, editors, Recent Advances in Iterative Methods, IMA Vol. 60, Springer, pages 95-119, 1993.
23. A. Greenbaum, V. Ptak and Z. Strakos. Any nonincreasing convergence curve is possible for GMRES. SIAM J. Matrix Anal. Appl., to appear.
24. M. H. Gutknecht. A completed theory of the unsymmetric Lanczos process and related algorithms, Part I. SIAM J. Matrix Anal. Appl., 13, 594-639, 1992.