Istituto di Scienza e Tecnologie dell'Informazione     
Arioli M., Codenotti B., Fassino C. Error analysis of three methods for computing the matrix exponential. In: Ercim Workshop on Numerical Linear Algebra Software Quality Principles and Techniques Theoretical and Experimental Aspects of Knowledge Representation. (Pisa, Italy, 21 - 22 May 1992). Proceedings, pp. 61 - 78. CNR-Pisa, ERCIM (eds.). ERCIM, 1992.
We analyze the Taylor and the Padé approximation methods and the Parlett method for computing the matrix exponential. We justify, with the analysis of the roundoff error, the well known result regarding the stability of the Taylor and the Padé methods, if the matrix norm is less than 1. Moreover, we characterize some classes of matrices, whose exponential is computed in a stable way by the Taylor and Padé algorithm; we also present for these matrices some upper bounds for the roundoff error.

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