Accurate and efficient matrix exponential computation

This work gives a new formula for the forward relative error of matrix exponential Taylor approximation and proposes new bounds for it depending on the matrix size and the Taylor approximation order, providing a new efficient scaling and squaring Taylor algorithm for the matrix exponential. A Matlab version of the new algorithm is provided and compared with Pade state-of-the-art algorithms obtaining higher accuracy in the majority of tests at similar or even lower cost.