Computing eigenvalues occurring in continuation methods with the Jacobi-Davidson QZ method

Journal of Computational Physics

Volumn 138, Issue 2, 1997, Pages 714-733

  Van Dorsselaer, Jos L M ^a  

^a UTRECHT UNIVERSITY   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS);

BIFURCATION POINTS; CONTINUATION METHOD; EIGEN-VALUE; GENERALIZED EIGENVALUE PROBLEMS; JACOBI- DAVIDSON; PHYSICAL PARAMETERS; RAYLEIGH; RAYLEIGH NUMBER; STATIONARY SOLUTIONS; TWO-DIMENSIONAL;

EIGENVALUES AND EIGENFUNCTIONS;

EID: 0031537360     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1997.5844     Document Type: Article

References (14)

1. Brand C. W. An incomplete-factorization preconditioning using repeated red-black ordering. Numer. Math. 61:1992;433.
2. Brown P. N., Saad Y. Hybrid Krylov methods for nonlinear systems of equations. SIAM J. Sci. Stat. Comput. 11:1990;450.
3. Dijkstra H. A., Molemaker M. J., van der Ploeg A., Botta E. F. F. An efficient code to compute non-parallel steady flows and their linear stability. Comput. Fluids. 24:1995;415.
4. Fokkema D. R., Sleijpen G. L. G., van der Vorst H. A. Accelerated inexact Newton schemes for large systems of nonlinear equations. SIAM J. Sci. Comput. 1995.
5. Fokkema D. R., Sleijpen G. L. G., van der Vorst H. A. Jacobi-Davidson style QR and QZ algorithms for the reduction of matrix pencils. SIAM J. Sci. Comput. 1997.
6. Golub G. H., van Loan C. F. Matrix Computations. 1989;John Hopkins Univ. Press, Baltimore.
7. van der Vorst H. A., Golub G. H. 150 Years old and still alive: Eigenproblems. The State of the Art in Numerical Analysis. 1997;Clarendon Press, Oxford. p. 93-.
8. Keller H. B. Numerical solution of bifurcation and nonlinear eigenvalue problems. Rabinowicz P. H. Applications of Bifurcation Theory. 1977;359 Academic Press, New York.
9. Saad Y., Schultz M. GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 7:1986;856.
10. Seydel R. Practical Bifurcation and Stability Analysis. 1994;Springer-Verlag, New York.
11. Sleijpen G. L. G., Booten A. G. L., Fokkema D. R., van der Vorst H. A. Jacobi-Davidson type methods for generalized eigenproblems and polynomial eigenproblems. BIT. 36:1996;595.
12. Sleijpen G. L. G., Fokkema D. R. BiCGstab(ℓ) for linear equations involving unsymmetric matrices with complex spectrum. Electron. Trans. Numer. Anal. (ETNA). 1:1993;11.
13. Stewart W. J., Jennings A. A simultaneous iteration algorithm for real matrices. ACM Trans. Math. Software. 7:1981;184.
14. Tiesinga G. Block preconditioned BiCGstab(2) for solving the Navier-Stokes equations. Z. Angew. Math. Mech. 76:1996;563.