Refined iterative algorithms based on Arnoldi's process for large unsymmetric eigenproblems

Linear Algebra and Its Applications

Volumn 259, Issue 1-3, 1997, Pages 1-23

  Jia, Zhongxiao ^a  

^a DALIAN UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038866149     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(96)00238-8     Document Type: Article

References (19)

1. W. E. Arnoldi, The principle of minimized iterations in the solution of the matrix eigenvalue problem, Quart. Appl. Math. 9:17-19 (1951).
2. Z. Bai, A collection of test matrices for large scale nonsymmetric eigenvalue problems, Version 1.0, 1994.
3. F. Chatelin and S. Godet-Thobie, Stability analysis in aeronautical industries, in Proceedings of the 2nd Symposium on High Performance Computing (M. Durand and F. E. Dabaghi, Eds.), Elsevier North-Holland, 1991, pp. 415-422.
4. J. W. Daniel, W. B. Gragg, L. Kaufman, and G. W. Stewart, Reorthogonalization and stable algorithms for updating the Gram-Schmidt factorization, Math. Comp. 30:772-795 (1976).
5. G. H. Golub and C. F. van Loan, Matrix Computations, 2nd ed., Johns Hopkins U.P., Baltimore, 1989.
6. D. Ho, Tchebychev acceleration technique for large scale nonsymmetric matrices, Numer. Math. 86:721-734 (1990).
7. Z. Jia, Studies on Convergence of Generalized Lanczos Methods for the Eigenproblems of Large Unsymmetric Matrices (in Chinese), Master's Thesis, Dalian Univ. of Technology, Dalian, 1987.
8. Z. Jia, The convergence of generalized Lanczos methods for large unsymmetric eigenproblems, SIAM J. Matrix Anal. Appl., 16:843-862 (1995).
9. Z. Jia, Generalized block Lanczos methods for large unsymmetric eigenproblems, Invited presentation at the Lanczos International Centenary Conference, Raleigh, N.C., 12-17 Dec. 1993; submitted for publication.
10. Z. Jia, Some Numerical Methods for Large Unsymmetric Eigenproblems, Ph.D. Thesis, Univ. of Bielefeld, Germany, 1994.
11. W. Kerner, Large-scale complex eigenvalue problems, J. Comput. Phys. 53:1-85 (1989).
12. C. Lanczos, An iteration method for the solution of the eigenvalue problem of linear differential and integral operators, J. Res. Nat. Bur. Standards 45:255-282 (1950).
13. A. Ruhe, The rational Krylov algorithm for nonsymmetric eigenvalue problems. III: Complex shifts for real matrices, BIT, 34:165-176 (1994).
14. A. Ruhe, Rational Krylov algorithms for nonsymmetric eigenvalue problems. II. Matrix pairs, Linear Algebra Appl. 197/198:283-296 (1994).
15. Y. Saad, Variations on Arnoldi's method for computing eigenelements of large unsymmetric matrices, Linear Algebra Appl. 34:269-295 (1980).
16. Y. Saad, Projection methods for solving large sparse eigenvalue problems, in Matrix Pencils (B. Kägström and A. Ruhe, Eds.), Springer-Verlag, Berlin, 1982, pp. 121-144.
17. Y. Saad, Chebyshev acceleration techniques for solving nonsymmetric eigenvalue problems, Math. Comp. 42:567-588 (1984).
18. Y. Saad, Numerical Method for Large Eigenvalue Problems, Manchester U.P., Manchester, 1992.
19. D. C. Sorensen, Implicit application of polynomial filters in a k-step Arnoldi method, SIAM J. Matrix Anal. Appl. 13:357-385 (1995).