Roundoff error analysis of algorithms based on Krylov subspace methods

BIT Numerical Mathematics

Volumn 36, Issue 2, 1996, Pages 189-205

  Arioli, M ^a   Fassino, C ^b  

^a CNR   (Italy)

^b UNIVERSITY OF ROME TOR VERGATA   (Italy)

Author keywords

GMRES; Krylov subspace methods; Roundoff error analysis

Indexed keywords

EID: 0011947356     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1007/bf01731978     Document Type: Article

References (21)

1. O. Axelsson, Conjugate gradient type methods for ansymmetric and inconsistent systems of equations, Linear Algebra Appl., 29 (1980), pp. 1-16.
2. P. N. Brown, A theoretical comparison of the Arnoldi and GMRES algorithms, SIAM J. Sci. Stat. Comput., 12 (1991), pp. 58-78.
3. P. Concus and G. H. Golub, A generalized conjugate gradient method for non-symmetric systems of linear equations, Tech. Rep. STAN-CS-76-535, Stanford University, Stanford CA, 1976.
4. J. Drkošová, A. Greenbaum, M, Rozložník, and Z, Strakoš, Numerical stability of GMRES, BIT 35 (1995), pp. 309-330.
5. S. C. Eisenstat, H. C. Elman, and M. H. Schultz, Variational iterative methods for nonsymmetric systems of linear equations, SIAM J. Numer. Anal., 20 (1983), pp.245-357.
6. H. C. Elman, Iterative Methods for Large Sparse Nonsymmetric Systems of Linear Equations, PhD thesis, Yale University, New Haven CT, 1982.
7. D. Goldberg, What every computer scientist should know about floating-point arithmetic, ACM Computing Surveys, 23, (1991), pp. 5-48.
8. G. H. Golub and C. VanLoan, Matrix Computations, 2nd ed., The Joans Hopkins University Press, Baltimore, MD, 1989.
9. K. C. Jea D. M.. Young, Generalized conjugate-gradient acceleration of non-symmetrizable iterative methods, Linear Algebra Appl., 34 (1980), pp. 159-194.
10. C. Lawson and R. Hanson, Solving Least Squares Problems, Prentice Hall, Englewood Cliffs, NJ, 1974.
11. N. M. Nachtigal, S. C. Reddy, and L. N. Trefethen, How fast are nonsymmetric matrix iterations?, SIAM J. Matrix. Anal. Appl. 13 (1992), pp. 778-795.
12. B. N. Parlett, The Symmetric Eigenvalue Problem, Prentice Hall, Englewood Cliffs, NJ, 1980.
13. Y. Saad, Numerical Methods for Large Eigenvalue problems, Manchester University Press, Manchester, UK, 1992.
14. Y. Saad and M. H. Schultz, Conjugate gradient-like algorithms for solving nonsymmetric linear systems, Math. Comp., 44 (1985), pp. 417-424.
15. _, GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. Sci. Statist. Comput., 7 (1986), pp. 856-869.
16. H. A. Van der Vorst, Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems, SIAM J. Sci. Stat. Comput., 13 (1992), pp. 631-644.
17. H. A. Van der Vorst, Lecture notes on iterative methods, Tech. Rep., CERFACS, Toulouse, France, 1992.
18. P. K. W. Vinsome, ORTHOMIN: an iterative method for solving sparse sets of simultaneous linear equations, in Proc. Fourth Symposium on Reservoir Simulation, Society of Petroleum Engineers of AIME, 1976, pp. 149-159.
19. H. F. Walker, Implementation of the GMRES method using Householder transformations, SIAM J. Sci. Stat. Comput., 9 (1988), pp. 152-163.
20. O. Widlund, A Lanczos method for a, class of nonsymmetric systems of linear equations, SIAM J. Numer. Anal., 15 (1978), pp. 801-812.
21. J. H. Wilkinson, The Algebraic Eigenvalue Problem, Clarendon Press, Oxford, UK, 1965.