矩阵指数计算算法讨论

对矩阵指数运算的ＰＳＳＡ方法与精细积分方法（ＰＩＭ）在实际应用中的最佳运算量等问题进行了讨论，可以发现，在一般情况下ＰＳＳＡ方法有较小的计算量，但其存在矩阵求逆问题；ＰＩＭ方法则具有无需矩阵求逆的特点，且算法由计算机位数限制造成的截断误差较ＰＳＳＡ方法的低，进一步对ＰＩＭ算法在２＾Ｎ运算中Ｎ值的选取与展开项数的选取提出了改进建议，这对于矩阵指数计算效率的提高是十分有益的。

Discussion about numerical computation of the matrix exponential

This paper gives a discussion about the computational cost and some other problems when the two numerical methods, i.e. Pade scaling and squaring approximation (PSSA), precise integration method (PIM), are used in the computation of the matrix exponential. It can be found that, in general, the PSSA has less computing time than PIM, but need an inverse computation of a matrix which will not exist in the PIM. Also, the roundoff error induced by computer in the PIM is smaller than that exists in the PSSA. Furthermore, the improvement for both the selection of parameter N and the item number in the Taylor series expansion for the 2 N computation algorithm of PIM is given in this paper, which is rather important for the computation of the matrix exponential.