Abstract
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.
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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.
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Xue, J., Ye, Q. Entrywise relative perturbation bounds for exponentials of essentially non-negative matrices. Numer. Math. 110, 393–403 (2008). https://doi.org/10.1007/s00211-008-0167-5
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DOI: https://doi.org/10.1007/s00211-008-0167-5