The Application For Computing The Rational Matrix Exponential By Symbolic Computation

In this paper we expound a method for computing matrix exponential (Ais the rational matrix ) by symbolic computation .For one random rationalmatrix A,it can be changed into the criterion:Because the process is rational,computing eA can be changed into computingeF.Then we can obtain eA through the equation:Because of the simple structure of Frobinus matrix,this procedure decreasethe working cost. And the process from eA to eF is accurate by symboliccomputation.We use two methods to compute eF.One way is that we obtain expectede?ect through Taylor series and Pade series and with the help of the Honerformula and the fundamental property of exponential function eF = (emF)m,but the working cost is heavy.The other way is formula method,which usesthat every element of matrix eF can be computed by a complex integral,andwhich have the function of parallel arithmetic.Althrough it can't avoid theproblem of working cost, we can easily find the source of error. And thenumerical example indicate these methods is useful.