Bounds of modulus of eigenvalues based on Stein equation

Guang-Da Hu; Qiao Zhu

Kybernetika (2010)

  • Volume: 46, Issue: 4, page 655-664
  • ISSN: 0023-5954

Abstract

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This paper is concerned with bounds of eigenvalues of a complex matrix. Both lower and upper bounds of modulus of eigenvalues are given by the Stein equation. Furthermore, two sequences are presented which converge to the minimal and the maximal modulus of eigenvalues, respectively. We have to point out that the two sequences are not recommendable for practical use for finding the minimal and the maximal modulus of eigenvalues.

How to cite

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Hu, Guang-Da, and Zhu, Qiao. "Bounds of modulus of eigenvalues based on Stein equation." Kybernetika 46.4 (2010): 655-664. <http://eudml.org/doc/196356>.

@article{Hu2010,
abstract = {This paper is concerned with bounds of eigenvalues of a complex matrix. Both lower and upper bounds of modulus of eigenvalues are given by the Stein equation. Furthermore, two sequences are presented which converge to the minimal and the maximal modulus of eigenvalues, respectively. We have to point out that the two sequences are not recommendable for practical use for finding the minimal and the maximal modulus of eigenvalues.},
author = {Hu, Guang-Da, Zhu, Qiao},
journal = {Kybernetika},
keywords = {eigenvalues; lower and upper bounds; Stein equation; eigenvalues; lower and upper bounds; Stein equation},
language = {eng},
number = {4},
pages = {655-664},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Bounds of modulus of eigenvalues based on Stein equation},
url = {http://eudml.org/doc/196356},
volume = {46},
year = {2010},
}

TY - JOUR
AU - Hu, Guang-Da
AU - Zhu, Qiao
TI - Bounds of modulus of eigenvalues based on Stein equation
JO - Kybernetika
PY - 2010
PB - Institute of Information Theory and Automation AS CR
VL - 46
IS - 4
SP - 655
EP - 664
AB - This paper is concerned with bounds of eigenvalues of a complex matrix. Both lower and upper bounds of modulus of eigenvalues are given by the Stein equation. Furthermore, two sequences are presented which converge to the minimal and the maximal modulus of eigenvalues, respectively. We have to point out that the two sequences are not recommendable for practical use for finding the minimal and the maximal modulus of eigenvalues.
LA - eng
KW - eigenvalues; lower and upper bounds; Stein equation; eigenvalues; lower and upper bounds; Stein equation
UR - http://eudml.org/doc/196356
ER -

References

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  14. Zhu, Q., Hu, G. D., Zeng, L., Estimating the spectral radius of a real matrix by discrete Lyapunov equation, J. Difference Equations Appl. To appear. 

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