On the Factorization of Hyperbolic and Unitary Transformations into Rotations

@article{Stewart2005OnTF,
  title={On the Factorization of Hyperbolic and Unitary Transformations into Rotations},
  author={Michael Stewart and Paul Van Dooren},
  journal={SIAM J. Matrix Analysis Applications},
  year={2005},
  volume={27},
  pages={876-890}
}
This paper presents a Σ-unitary analogue to the CS decomposition of a partitioned unitary matrix. The hyperbolic rotations revealed by the decomposition are shown to be optimal in that, among a broader class of decompositions of Σ-unitary matrices into elementary hyperbolic rotations, they are the smallest possible in a sum-of-squares sense. A similar optimality property is shown to hold for the sines in the CS decomposition of a unitary matrix. 

From This Paper

Topics from this paper.
2 Citations
8 References
Similar Papers

Citations

Publications citing this paper.
Showing 1-2 of 2 extracted citations

References

Publications referenced by this paper.
Showing 1-8 of 8 references

On hyperbolic triangularization: Stability and pivoting

  • M. Stewart, G. W. Stewart
  • SIAM J. Matrix Anal. Appl., 19
  • 1998
2 Excerpts

Block downdating of least squares solutions

  • L. Eldén, H. Park
  • SIAM J. Matrix Anal. Appl., 15
  • 1994
2 Excerpts

The rotation of eigenvectors by a perturbation

  • C. Davis, W. M. Kahan
  • III, SIAM J. Numer. Anal., 7
  • 1970
2 Excerpts

The rotation of eigenvectors by a perturbation . III

  • T. A. Arias Edelman, S. T. Smith
  • SIAM J . Numer . Anal .
  • 1970

Similar Papers

Loading similar papers…