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