full
search.png

Search

close.png

Cancel

arrow
Volume 26, Issue 2
The Sensitivity of the Exponential of an Essentially Nonnegative Matrix

Weifang Zhu, Jungong Xue & Weiguo Gao

J. Comp. Math., 26 (2008), pp. 250-258.

Published online: 2008-04

Preview Full PDF 2577 25939

Cited by

google scholar semantic scholar
Export citation
  • Abstract

This paper performs perturbation analysis for the exponential of an essentially nonnegative matrix which is perturbed in the way that each entry has a small relative perturbation. For a general essentially nonnegative matrix, we obtain an upper bound for the relative error in $2$-norm, which is sharper than the existing perturbation results. For a triangular essentially nonnegative matrix, we obtain an upper bound for the relative error in entrywise sense. This bound indicates that, if the spectral radius of an essentially nonnegative matrix is not large, then small entrywise relative perturbations cause small relative error in each entry of its exponential. Finally, we apply our perturbation results to the sensitivity analysis of RC networks and complementary distribution functions of phase-type distributions.

  • Keywords

Essentially nonnegative matrix, Matrix exponential, Entrywise perturbation theory, RC network, Phase-type distribution.

  • AMS Subject Headings

65F35, 15A42.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{JCM-26-250, author = {Weifang Zhu, Jungong Xue and Weiguo Gao}, title = {The Sensitivity of the Exponential of an Essentially Nonnegative Matrix}, journal = {Journal of Computational Mathematics}, year = {2008}, volume = {26}, number = {2}, pages = {250--258}, abstract = {

This paper performs perturbation analysis for the exponential of an essentially nonnegative matrix which is perturbed in the way that each entry has a small relative perturbation. For a general essentially nonnegative matrix, we obtain an upper bound for the relative error in $2$-norm, which is sharper than the existing perturbation results. For a triangular essentially nonnegative matrix, we obtain an upper bound for the relative error in entrywise sense. This bound indicates that, if the spectral radius of an essentially nonnegative matrix is not large, then small entrywise relative perturbations cause small relative error in each entry of its exponential. Finally, we apply our perturbation results to the sensitivity analysis of RC networks and complementary distribution functions of phase-type distributions.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8622.html} }
TY - JOUR T1 - The Sensitivity of the Exponential of an Essentially Nonnegative Matrix AU - Weifang Zhu, Jungong Xue & Weiguo Gao JO - Journal of Computational Mathematics VL - 2 SP - 250 EP - 258 PY - 2008 DA - 2008/04 SN - 26 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8622.html KW - Essentially nonnegative matrix, Matrix exponential, Entrywise perturbation theory, RC network, Phase-type distribution. AB -

This paper performs perturbation analysis for the exponential of an essentially nonnegative matrix which is perturbed in the way that each entry has a small relative perturbation. For a general essentially nonnegative matrix, we obtain an upper bound for the relative error in $2$-norm, which is sharper than the existing perturbation results. For a triangular essentially nonnegative matrix, we obtain an upper bound for the relative error in entrywise sense. This bound indicates that, if the spectral radius of an essentially nonnegative matrix is not large, then small entrywise relative perturbations cause small relative error in each entry of its exponential. Finally, we apply our perturbation results to the sensitivity analysis of RC networks and complementary distribution functions of phase-type distributions.

Weifang Zhu, Jungong Xue and Weiguo Gao. (2008). The Sensitivity of the Exponential of an Essentially Nonnegative Matrix. Journal of Computational Mathematics. 26 (2). 250-258. doi:
Copy to clipboard
BibteX RIS TXT
The citation has been copied to your clipboard