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C. B. Moler and C. F. Van Loan, “Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later,” SIAM Review, Vol. 45, No. 1, 2003, pp. 3-49. doi:10.1137/S00361445024180

has been cited by the following article:

• TITLE: Matrix Padé-Type Method for Computing the Matrix Exponential

  AUTHORS: Chunjing Li, Xiaojing Zhu, Chuanqing Gu

  KEYWORDS: Matrix PadÉ-Type Approximation, Matrix Exponential, Scaling and Squaring, Backward Er-ror

  JOURNAL NAME: Applied Mathematics, Vol.2 No.2, February 25, 2011

  ABSTRACT: 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 and for computing with many espectively. 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 . 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 for a fixed matrix A with many t ≥ 0.