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Articles

New upper bounds for the spectral variation of a general matrix

Pages 3070-3080 | Received 12 Jul 2020, Accepted 10 Aug 2020, Published online: 20 Sep 2020

References

  • Bhatia R. Perturbation bounds for matrix eigenvalues. Philadelphia: SIAM; 2007.
  • Bhatia R, Kittaneh F, Li R-C. Some inequalities for commutators and an application to spectral variation. II. Linear Multilinear Algebra. 1997;43:207–219. doi: 10.1080/03081089708818526
  • Eisenstat SC, Ipsen ICF. Three absolute perturbation bounds for matrix eigenvalues imply relative bounds. SIAM J Matrix Anal Appl. 1998;20:149–158. doi: 10.1137/S0895479897323282
  • Elsner L, Friedland S. Singular values, doubly stochastic matrices, and applications. Linear Algebra Appl. 1995;220:161–169. doi: 10.1016/0024-3795(95)00111-4
  • Hoffman AJ, Wielandt HW. The variation of the spectrum of a normal matrix. Duke Math J. 1953;20:37–39. doi: 10.1215/S0012-7094-53-02004-3
  • Ipsen ICF. Relative perturbation results for matrix eigenvalues and singular values. Acta Numer. 1998;7:151–201. doi: 10.1017/S0962492900002828
  • Li R-C. Relative perturbation theory: I. eigenvalue and singular value variations. SIAM J Matrix Anal Appl. 1998;19:956–982. doi: 10.1137/S089547989629849X
  • Li W, Chen J-X. The eigenvalue perturbation bound for arbitrary matrices. J Comput Math. 2006;24:141–148.
  • Li W, Sun W. The perturbation bounds for eigenvalues of normal matrices. Numer Linear Algebra Appl. 2005;12:89–94. doi: 10.1002/nla.400
  • Li W, Vong S-W. On the variation of the spectrum of a Hermitian matrix. Appl Math Lett. 2017;65:70–76. doi: 10.1016/j.aml.2016.10.005
  • Song Y. A note on the variation of the spectrum of an arbitrary matrix. Linear Algebra Appl. 2002;342:41–46. doi: 10.1016/S0024-3795(01)00447-5
  • Sun J-G. On the variation of the spectrum of a normal matrix. Linear Algebra Appl. 1996;246:215–223. doi: 10.1016/0024-3795(94)00354-8
  • Xu X, Zhang C-S. New perturbation bounds for the spectrum of a normal matrix. J Math Anal Appl. 2017;455:1937–1955. doi: 10.1016/j.jmaa.2017.06.051

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