An efficient bound for the condition number of the matrix exponential

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An Efficient Bound for the Condition Number of the Matrix Exponential

A new bound for the condition number of the matrix exponential is presented. Using the bound, we propose an efficient approximation to the condition number, denoted by κg(s,X), that avoids the computation of the Fréchet derivative of the matrix exponential that underlies condition number estimation in the existing algorithms. We exploit the identity eX = (eX/2 s )2 s for a nonnegative integer s...

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Computing the Fréchet Derivative of the Matrix Exponential, with an Application to Condition Number Estimation

The matrix exponential is a much-studied matrix function having many applications. The Fréchet derivative of the matrix exponential describes the first-order sensitivity of eA to perturbations in A and its norm determines a condition number for eA. Among the numerous methods for computing eA the scaling and squaring method is the most widely used. We show that the implementation of the method i...

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ژورنال

عنوان ژورنال: Journal of Taibah University for Science

سال: 2017

ISSN: 1658-3655

DOI: 10.1016/j.jtusci.2015.10.006