Backward errors and small-sample condition estimation for ⋆-Sylveter equations

Huai An Diao, Wei-Hong Yan, Eric King wah Chu

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5 Citations (Scopus)


In this paper, we consider the perturbation analysis for ⋆-Sylvester equations. Based on the small-sample condition estimation (SCE) technique, we devise algorithms to estimate normwise, mixed and componentwise condition numbers for ⋆-Sylvester equations. We also define a componentwise backward error with a sharp and easily computable bound. Numerical examples illustrate that our algorithm for componentwise perturbations produces reliable estimates, and the new derived computable bound for the componentwise backward error is sharp and reliable for well-conditioned and moderate ill-conditioned ⋆-Sylvester equations under large or small perturbations.

Original languageEnglish
Pages (from-to)2106-2121
Number of pages16
JournalInternational Journal of Computer Mathematics
Issue number10
Publication statusPublished - 3 Oct 2017


  • backward error
  • componentwise perturbation
  • condition number
  • small-sample condition estimation
  • ⋆-Sylvester equation

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