连分式逼近与多项式逼近的计算效果比较研究

摘要

It is observed and analyzed on the effect of approximate calculation of continued fraction ap-proximation and polynomial approximation in many ways in this paper .An irrational number was approxi-mated by using continued fraction approximation and Maclaurin series at first .Then approximating a func-tion was taken into account .Through comparisons of numerical results , continued fraction approximation has excellences of rapid convergence ,high precision ,large convergent domain and so on in contrast to pol-ynomial approximation .Continued fraction approximation and polynomial approximation are two classic tools for approximating function and play an important role in numerical calculation .%从多方面观察和比较连分式逼近与多项式逼近的近似计算效果，首先利用连分式与Maclaurin级数逼近无理数，其次考虑了对函数的逼近。通过数值实例的比较，由此可以看出连分式逼近相对多项式的逼近具有收敛速度快、计算精度高以及收敛域广等特点。连分式与多项式级数是两个经典的逼近函数的工具，在数值计算中有着重要作用。