Current inverse iteration software can fail

BIT Numerical Mathematics

Volumn 38, Issue 4, 1998, Pages 685-704

  Dhillon, Inderjit S ^a,b  

^a IBM ALMADEN RESEARCH CENTER   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Eigenvalues; Eigenvectors; Inverse iteration; Symmetric; Tridiagonal matrix

Indexed keywords

EID: 0348229160     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02510409     Document Type: Article

References (20)

1. E. Anderson, Z. Bai, C. Bischof, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, S. Ostrouchov, and D. Sorensen, LAPACK Users' Guide, 2nd. ed., SIAM, Philadelphia, PA, 1995.
2. S. Chandrasekaran, When is a Linear System Ill-Conditioned? PhD thesis, Department of Computer Science, Yale University, New Haven, CT, 1994.
3. S. Chandrasekaran, 1996, private communication.
4. J. Demmel and A. McKenney, A test matrix generation suite, Tech. Report, Computer Science Department, Courant Institute, New York, NY, July 1989 (LAPACK Working Note #9).
5. 2) Algorithm for the Symmetric Tridiagonal Eigenvalue/Eigenvector Problem, PhD thesis, University of California, Berkeley, CA, May 1997.
6. I. S. Dhillon and B. N. Parlett, Computing the eigenvectors of a symmetric tridiagonal matrix, in preparation.
7. J. Du Croz, December 1994, private communication.
8. K. V. Fernando, On computing an eigenvector of a tridiagonal matrix part I: Basic results, SIAM J. Matrix Anal. Appl., 18:4 (1997), pp. 1013-1034.
9. S. K. Godunov, A. G. Antonov, O. P. Kiriljuk, and V. I. Kostin, Guaranted Accuracy in Numerical Linear Algebra, Kluwer Academic Publishers, Dordrecht, 1993. A revised translation of a Russian text first published in 1988 in Novosibirsk.
10. S. K. Godunov, V. I. Kostin, and A. D. Mitchenko, Computation of an eigenvector of symmetric tridiagonal matrices, Siberian Math. J., 26 (1985), pp. 71-85.
11. A. S. Householder, Unitary triangularization of a nonsymmetric matrix, J. ACM., 5 (1958), pp. 339-342.
12. I. C. F. Ipsen, Computing an eigenvector with inverse iteration, SIAM Review, 39:2 (1997), pp. 254-291.
13. E. Jessup and I. C. F. Ipsen, Improving the accuracy of inverse iteration, SIAM J. Sci. Stat. Comput., 13:2 (1992), pp. 550-572.
14. B. N. Parlett, The Symmetric Eigenvalue Problem, 2nd ed., SIAM, Philadelphia, PA, 1997.
15. B. N. Parlett and I. S. Dhillon, Fernando's solution to Wilkinson's problem: An application of double factorization, Linear Algebra Appl., 267 (1997), pp. 247-279.
16. G. Peters and J. H. Wilkinson, The calculation of specified eigenvectors by inverse iteration, contribution II/18, Vol. II of Handbook of Automatic Computation, Springer-Verlag, Berlin, 1971, pp. 418-439.
17. G. Peters and J. H. Wilkinson, Inverse iteration, ill-conditioned equations and Newton's method, SIAM Review, 21 (1979), pp. 339-360.
18. B. T. Smith, J. M. Boyle, J. J. Dongarra, B. S. Garbow, Y. Ikebe, V. C. Klema, and C. B. Moler, Matrix Eigensystem Routines - EISPACK Guide, Lecture Notes in Computer Science, Vol. 6, Springer-Verlag, Berlin, 1976.
19. J. H. Wilkinson, The calculation of the eigenvectors of codiagonal matrices, Computer J., 1 (1958), pp. 90-96.
20. J. H. Wilkinson, The Algebraic Eigenvalue Problem, Oxford University Press, Oxford, 1965.