A Numerical Investigation of Different Methods for Computing the Matrix Exponential

Sammanfattning: Matrix functions and their applications play an important role in different fields of science and engineering. The matrix exponential is one of the most important and extensively used function of matrices. The computation of the exponential of a matrix is an interesting topic that has been extensively studied over the years. There are several ways computing the matrix exponential but there is a puzzle about which method is best. The foundation of this thesis project is a classic paper from 1978 which highlights most of these methods. An updated version was published in 2003. There have been further improvements on these methods since then but the core algorithms remain the same, hence the paper is still relevant. This thesis project is devoted to implementing the various methods of computing the matrix exponential, comparing these methods, and finally determining the best method in terms of generality, reliability, stability, accuracy, and efficiency.