Entrywise relative perturbation bounds for exponentials of essentially non-negative matrices

Jungong Xue, Qiang Ye

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


A real square matrix is said to be essentially non-negative if all of its off-diagonal entries are non-negative. We establish entrywise relative perturbation bounds for the exponential of an essentially non-negative matrix. Our bounds are sharp and contain a condition number that is intrinsic to the exponential function. As an application, we study sensitivity of continuous-time Markov chains.

Original languageEnglish
Pages (from-to)393-403
Number of pages11
JournalNumerische Mathematik
Issue number3
StatePublished - Sep 2008

Bibliographical note

Funding Information:
J. Xue was supported by the National Science Foundation of China under grant number 10571031, the Program for New Century Excellent Talents in Universities of China and Shanghai Pujiang Program. Q. Ye was supported in part by NSF under Grant DMS-0411502.

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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