误差函数Chebyshev级数的计算方法

Chebyshev series method for the error function

为了在IEEE浮点计算环境下对误差函数进行精确有效地赋值,提出了误差函数的Chebyshev级数计算方法。采用Clenshaw算法计算级数的前N项部分和,减小求和的舍入误差。实验结果表明,针对误差函数的赋值问题,Chebyshev级数比Taylor级数的收敛速度更快,即达到相同的赋值精度要求时,Chebyshev级数法需要的项数远少于Taylor级数法。

In order to evaluate error function efficiently and accurately in the IEEE floating-point arithmetic environment.This paper investigates the Chebyshev series expansion method for the evaluation of the error function.In addition,using Clenshaw algorithm to compute the partial sum of the first Nterms leads to the rounding errors reduction.The experimental results show that Chebyshev series method has faster convergence speed than Taylor series method.In other words,to attain the same computation precision Chebyshev method needs fewer terms than Taylor method.