A Kind Of Accurate Expression Of The Rational Matrix Exponential

In this paper, we mainly discuss the problem of computing rational matrixexponential. The most important achievement is that we expound a new methodfor computing rational matrix exponential by symbolic computation. With thenew method,we can work out a kind of accurate expression of the rational matrixexponential. Exploiting the software Mathematica, we can also get any accurateresult up to 100000 decimal places.This paper is divided into three chapters. Chapter 1 resumptively intro-duces the origin and actuality about the computation of matrix exponential,then recounts the origin and significance of the symbolic computation. Chapter2 summarizes the existent methods that can compute matrix exponential. Theyall are numerical value method. It will produce abundant errors to computematrix exponential with these methods, which leads the accuracy of result bad.Chapter 3, the most important one, introduces the academic gists that computerational matrix exponential by symbolic computation and algorithm in detail,which deduces a new method. Finally, we compare the new method with the oldones by a numerical value example, the result show that the new method is verysuper in the accuracy of computation.