Relative perturbation bounds for the unitary polar factor

BIT Numerical Mathematics

Volumn 37, Issue 1, 1997, Pages 67-75

  Li, Ren Cang ^a  

^a OAK RIDGE NATIONAL LABORATORY   (United States)

Author keywords

Polar decomposition; Relative perturbation theory; Scaling

Indexed keywords

EID: 0442293617     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02510173     Document Type: Article

References (15)

1. J. Barlow and J. Demmel, Computing accurate eigensystems of scaled diagonally dominant matrices, SIAM J. Numer. Anal., 27 (1990), pp. 762-791.
2. A. Barrlund, Perturbation bounds on the polar decomposition, BIT, 30 (1990), pp. 101-113.
3. C.-H. Chen and J.-G. Sun, Perturbation bounds for the polar factors, J. Comp. Math., 7 (1989), pp. 397-401.
4. J. Demmel and W. Gragg, On computing accurate singular values and eigenvalues of matrices with acyclic graphs, Linear Algebra Appl., 185 (1993), pp. 203-217.
5. J. Demmel and W. Kahan, Accurate singular values of bidiagonal matrices, SIAM J. Sci. Stat. Comput., 11 (1990), pp. 873-912.
6. N. J. Higham, Computing the polar decomposition - with applications, SIAM J, Sci. Stat. Comput., 7 (1986), pp. 1160-1174.
7. W. Kahan, Accurate eigenvalues of a symmetric tridiagonal matrix, Tech. Report CS41, Computer Science Department, Stanford University, Stanford, CA, 1966 (revised June 1968).
8. C. Kenney and A. J. Laub, Polar decompostion and matrix sign function condition estimates, SIAM J. Sci. Stat. Comput., 12 (1991), pp. 488-504.
9. F. Kittaneh, Inequalities for the schatten p-norm. III, Comm. Math. Phys., 104 (1986), pp. 307-310.
10. R.-C. Li, A perturbation bound for the generalized polar decomposition, BIT, 33 (1993), pp. 304-308.
11. R.-C. Li, Relative perturbation theory: (II) eigenspace and singular subspace variations, Tech. Report UCB//CSD-94-856, Computer Science Division, Department of EECS, University of California at Berkeley, 1994 (revised January 1996 and April 1996).
12. R.-C. Li, New perturbation bounds for the unitary polar factor, SIAM J. Matrix Anal. Appl., 16 (1995), pp. 327-332.
13. H, J. Comp. Math., 4 (1986), pp. 245-248.
14. R. Mathias, Perturbation bounds for the polar decomposition, SIAM J. Matrix Anal. Appl., 14 (1993), pp. 588-597.
15. J.-G. Sun and C.-H. Chen, Generalized polar decomposition, Math. Numer. Sinica, 11 (1989), pp. 262-273. In Chinese.