Relative Perturbation Theory: Iv Sin 2 Theorems 1 Relative Perturbation Theory: Iv Sin 2 Theorems

@inproceedings{Li1999RelativePT,
  title={Relative Perturbation Theory: Iv Sin 2 Theorems 1 Relative Perturbation Theory: Iv Sin 2 Theorems},
  author={Ren-Cang Li},
  year={1999}
}
The double angle theorems of Davis and Kahan bound the change in an invariant subspace when a Hermitian matrix A is subject to an additive perturbation A ! e A = A+A. This paper supplies analogous results when A is subject to a congruential, or multiplicative, perturbation A ! e A = D AD. The relative gaps that appear in the bounds involve the spectrum of only one matrix, either A or e A, in contrast to the gaps that appear in the single angle bounds. The double angle theorems do not directly… CONTINUE READING

References

Publications referenced by this paper.
Showing 1-10 of 24 references

Perturbation bounds for eigenspaces of a de nite matrix pair

  • J.-G. Sun
  • Numerische Math- ematik, 41
  • 1983
Highly Influential
7 Excerpts

A new relative perturbation theorem for singular subspaces

  • R.-C. Li, G. W. Stewart
  • Linear Algebra and its Application,
  • 1999
Highly Influential
7 Excerpts

Relative perturbation results for matrix eigenvalues and singular values

  • I.C.F. Ipsen
  • Acta Numerica, 7
  • 1998
Highly Influential
13 Excerpts

Relative perturbation bounds for eigenspaces and singular vector subspaces

  • S. C. Eisenstat, I.C.F. Ipsen
  • Proceedings of the Fifth SIAM Conference on…
  • 1994
Highly Influential
15 Excerpts

The rotation of eigenvectors by a perturbation

  • C. Davis, W. Kahan
  • III, SIAM Journal on Numerical Analysis, 7
  • 1970
Highly Influential
4 Excerpts

An implementation of the dqds algorithm (positive case)

  • B. N. Parlett, O. A. Marques
  • submitted for publication
  • 1999
2 Excerpts

I

  • J. W. Demmel, M. Gu, S. C. Eisenstat
  • Slapni car, K. Veseli c, and Z. Drma c…
  • 1999
2 Excerpts

Similar Papers

Loading similar papers…