分段混合阶修正Padé逼近及指数函数计算

摘要

结合Pad▽逼近和分段插值的概念,提出了一种分段混合阶修正Padé逼近,给出了计算公式.其优点在于:精确度高,而且具有局部可控性,可以通过增加逼近阶数或插值节点来提高逼近的精度.数值结果表明,该方法逼近指数函数优于其它一些有理方法.%A piecewise modified Padé approximation of hybrid order,which combines Padé approximation and piecewise interpolation concept,is introduced in this paper.The explicit formulation is presented.It has two advantages:high accuracy and local controllability.The accuracy of this approximation increases as the order or the node increases.The numerical results are given to show that the presented method is superior to some other rational methods by applying them to approximate the exponential function.