Matrix Padé-Type Method for Computing the Matrix Exponential

Matrix Padé approximation is a widely used method for computing matrix functions. In this paper, we apply matrix Padé-type approximation instead of typical Padé approximation to computing the matrix exponential. In our approach the scaling and squaring method is also used to make the approximant more accurate. We present two algorithms for computing A e and for computing At e with many 0 t  respectively. Numerical experiments comparing the proposed method with other existing methods which are MATLAB’s functions expm and funm show that our approach is also very effective and reliable for computing the matrix exponential A e . Moreover, there are two main advantages of our approach. One is that there is no inverse of a matrix required in this method. The other is that this method is more convenient when computing At e for a fixed matrix A with many 0 t  .