Optimal perturbation bounds for the Hermitian eigenvalue problem

Linear Algebra and Its Applications

Volumn 309, Issue 1-3, 2000, Pages 19-43

  Barlow, Jesse L ^a   Slapničar, Ivan ^b  

^a The Pennsylvania State University   (United States)

^b UNIVERSITY OF SPLIT   (Croatia)

Author keywords

Absolute gap; Pseudoinverse; Relative error; Relative gap; Zero subspace

Indexed keywords

EID: 0346042887     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(99)00268-2     Document Type: Article

References (19)

1. Barlow J.L., Demmel J.W. Computing accurate eigensystems of scaled diagonally dominant matrices. SIAM J. Numer. Anal. 27:1990;762-791.
2. J.L. Barlow, I. Slapničar, Optimal perturbation bounds for the Hermitian eigenvalue problem, Technical report, The Pennsylvania State University, 1999.
3. S.L. Campbell Jr., C.D. Meyer, Generalized Inverses of Linear Transformations, Pitman, London, 1979. Reprint by Dover, New York, 1991.
4. Davis C., Kahan W.M. The rotation of eigenvectors by a perturbation III. SIAMJ.Num.Anal. 7:1970;1-46.
5. Demmel J.W., Veselić K. Jacobi's method is more accurate than QR. SIAM J. Matrix Anal. Appl. 13:1992;1204-1243.
6. F.M. Dopico, J. Moro, J.M. Molera, Weyl-type perturbation bounds for eigenvalues of Hermitian matrices, 1998, preprint.
7. Eisenstat S.C., Ipsen I.C.F. Relative perturbation techniques for singular value problems. SIAMJ. Numer. Anal. 32:1995;1972-1988.
8. Eldén L. Error analysis of direct method of matrix inversion. J. ACM. 8:1961;281-330.
9. G.H. Golub, C.F. Van Loan, Matrix Computations, second edition, The Johns Hopkins Press, Baltimore, 1989.
10. M. Gu, Studies in Numerical Linear Algebra, Ph.D. thesis, Yale University, New Haven, CT, 1994.
11. M. Gu, S.C. Eisenstat, Relative perturbation theory for eigenproblems, Research Report YALEU/DCS/RR-934, Department of Computer Science, Yale University, New Haven, CT, February 1993.
12. T. Kato, A Short Introduction to Perturbation Theory for Linear Operators, Springer, New York, 1982.
13. Li R.-C. Relative perturbation theory: (i) Eigenvalue and singular value variations. SIAM J. Matrix Anal. Appl. 19:1998;956-982.
14. Li R.C. Relative perturbation theory: (ii) Eigenspace and singular subspace variations. SIAMJ. Matrix Anal. Appl. 20:1998;471-492.
15. C.F. Van Loan, Generalizing the singular value decomposition, SIAM J. Num. Anal. 13 (1976) 76-83.
16. Paige C.C., Saunders M.A. Towards a generalized singular value decomposition. SIAM J. Num. Anal. 18:1981;398-405.
17. B.N. Parlett, The Symmetric Eigenvalue Problem, Prentice-Hall, Englewood Cliffs, NJ, 1980.
18. Veselić K., Slapničar I. Floating-point perturbations of Hermitian matrices. Linear Algebra Appl. 195:1993;81-116.
19. J.H. Wilkinson, The Algebraic Eigenvalue Problem, Oxford University Press, London, 1965.