函数exp(q)的padé逼近的A(α)-可接受性

A(α)-ACCEPTABILITY OF PADé APPROXIMATIONS TO FUNCTION EXP(Q)

本文主要讨论了函数exp（q）的pade逼近的A（α）-可接受性．对a∈（0，π／2），m≥n，m≥2，得到了exp（q）的有理逼近R（q）为A（α）-可接受的充要条件和paed逼近（q）为A（α）-可接受的几个充分条件．证明了（q）是A（π／3）-可接受的．文末构造了5阶A（π／3）-稳定的四阶导数单步方法与三阶导数混合单步法．

In this Paper, we have got the necessary and sufficient conditions off A(α)-accept- ability for rational approximations to the fuction exp (q). Some sufficient conditions to guarantee A(α)-acceptability of Pade approximations R(q) to function exp(q) were giren, where a∈(0,π/2), m≥n,m≥2. Furthermore,the condition of A(α)-acceptability of rational approximations to exp (q) isepuivalent to the nonnegativity of of a real polynomial. Finally, the auther proved that R(q) is A(π／3)-acceptable.By this two A(π／3) -stable multiderivative (hybrid) one-step methods are constructed.