Homotopy continuation algorithm for the real nonsymmetric eigenproblem: further development and implementation

SIAM Journal of Scientific Computing

Volumn 20, Issue 5, 1999, Pages 1627-1651

  Li, T Y ^a   Zeng, Zhonggang ^b  

^a MICHIGAN STATE UNIVERSITY   (United States)

^b NORTHEASTERN ILLINOIS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); CODES (SYMBOLS); EIGENVALUES AND EIGENFUNCTIONS; ITERATIVE METHODS; MATRIX ALGEBRA; PROBLEM SOLVING;

HOMOTOPY CONTINUATION ALGORITHMS; NONSYMMETRIC EIGENVALUE PROBLEMS;

PARALLEL ALGORITHMS;

EID: 0033295132     PISSN: 10648275     EISSN: None     Source Type: None    
DOI: 10.1137/S1064827597318228     Document Type: Article

References (17)

1. L. AUSLANDER AND A. TSAO, On parallelizable eigensolvers, Adv. Appl. Math., 13 (1992), pp. 253-261.
2. E. ANDERSON, Z. BAI, C. BISCHOF, J. DEMMEL, J. DONGARRA, J. D. CROZ, A. GREENBAUM, S. HAMMARLING, A. MCKENNEY, AND D. SORENSON, LAPACK Users' Guide, SIAM, Philadelphia, 1992.
3. Z. BAI, R. BARRETT, D. DAY, J. DEMMEL, AND J. DONGARRA, Test Matrix Collection (Non-Hermitian Eigenvalue Problems), preprint, University of Kentucky, Lexington, KY, 1995.
4. Z. BAI AND J. DEMMEL, Design of a parallel nonsymmetric eigenroutine toolbox, part I, in Proc. Sixth SIAM Conf. on Parallel Processing for Scientific Computing, vol. 1, R. F. Sincovec, D. E. Keyes, M. R. Leuze, L. R. Petzold, and D. A. Reed, eds., SIAM, Philadelphia, 1993, pp. 391-398.
5. J. J. DONGARRA AND M. SIDANI, A parallel algorithm for the nonsymmetric eigenvalue problem, SIAM J. Sci. Comput., 14 (1993), pp. 542-569.
6. Q. DU, M. JIN, T. Y. LI, AND Z. ZENG, The quasi-Laguerre iteration, J. Math. Comput., 66 (1997), pp. 345-361.
7. Q. DU, M. JIN, T. Y. LI, AND Z. ZENG, Quasi-Laguerre iteration in solving symmetric tridiagonal eigenvalue problems, SIAM J. Sci. Comput., 17 (1996), pp. 1347-1368.
8. G. HENRY AND R. VAN DE GEIJN, Parallelizing the QR algorithm for the unsymmetric algebraic eigenvalue problem: Myths and reality, SIAM J. Sci. Comput., 17 (1996), pp. 870-883.
9. M. A. HYMAN, Eigenvalues and eigenvectors of general matrices, in 12th National Meeting ACM, Houston, TX, 1957.
10. W. KAHAN, Notes on Laguerre's Iteration, preprint, University of California, Berkeley, CA, 1992.
11. S. HUSS-LEDERMAN, A. TSAO, AND T. TURNBULL, A parallelizable eigensolver for real diagonalizable matrices with real eigenvalues, SIAM J. Sci. Comput., 18 (1997), pp. 869-885.
12. T. Y. LI, Z. ZENG, AND L. CONG, Solving eigenvalue problems of real nonsymmetric matrices with real homotopies, SIAM J. Numer. Anal., 29 (1992), pp. 229-248.
13. T. Y. LI AND Z. ZENG, Homotopy-determinant algorithm solving nonsymmetric eigenvalue problems, Math. Comp., 59 (1992), pp. 483-502.
14. D. G. LUENBERGER, Linear and Nonlinear Programming, 2nd ed., Addison-Wesley, Reading, MA, 1989.
15. Y. SAAD, Numerical Methods for Large Eigenvalue Problems, Halsted Press, New York, 1992.
16. J. H. WILKINSON, The Algebraic Eigenvalue Problem, Oxford University Press, New York, 1965.
17. Z. ZENG, Homotopy-determinant Method for Solving Matrix Eigenvalue Problems and Its Parallelizations, Ph.D. thesis, Michigan State University, East Lansing, MI, 1991.