A new efficient and accurate spline algorithm for the matrix exponential computation, Emilio Defez, Javier Ibáñez, Jorge Sastre, Jesús Peinado, Pedro Alonso. Journal of Computational and Applied Mathematics, Volume 337, pp. 354-365. August 2018. Preprint, Matlab code expmspl.m.
In this work an accurate and efficient method based on matrix splines for computing matrix exponential is given. An algorithm and a MATLAB implementation have been developed and compared with the state-of-the-art algorithms for computing the matrix exponential. We also developed a parallel implementation for large scale problems. This implementation allowed us to get a much better performance when working with this kind of problems.