Weyl-type relative perturbation bounds for eigensystems of Hermitian matrices

@article{Dopico2000WeyltypeRP,
  title={Weyl-type relative perturbation bounds for eigensystems of Hermitian matrices},
  author={F. Dopico and J. Moro and J. M. Molera},
  journal={Linear Algebra and its Applications},
  year={2000},
  volume={309},
  pages={3-18}
}
We present a Weyl-type relative bound for eigenvalues of Hermitian perturbations A+E of (not necessarily definite) Hermitian matrices A. This bound, given in function of the quantity η=∥A−1/2EA−1/2∥2, that was already known in the definite case, is shown to be valid as well in the indefinite case. We also extend to the indefinite case relative eigenvector bounds which depend on the same quantity η. As a consequence, new relative perturbation bounds for singular values and vectors are also… Expand
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References

SHOWING 1-10 OF 27 REFERENCES
Three Absolute Perturbation Bounds for Matrix Eigenvalues Imply Relative Bounds
  • 69
  • Highly Influential
Perturbation bounds in connection with singular value decomposition
  • 373
  • Highly Influential
Relative perturbation techniques for singular value problems
  • 118
Spectral Perturbation Bounds for Positive Definite Matrices
  • 30
  • Highly Influential
Relative Perturbation Theory: I. Eigenvalue and Singular Value Variations
  • 135
  • PDF
The Lidskii-Mirsky-Wielandt theorem – additive and multiplicative versions
  • 41
  • PDF
Relative Perturbation Theory: II. Eigenspace and Singular Subspace Variations
  • R. Li
  • Mathematics, Computer Science
  • SIAM J. Matrix Anal. Appl.
  • 1998
  • 149
  • PDF
...
1
2
3
...