误差函数Chebyshev级数的计算方法  

Chebyshev series method for the error function

作　　者：邓国强[1,2] 唐敏[1,2] DENG Guoqiang TANG Min(School of Mathematics and Computing Science, Guilin University of Electrical Technology, Guilin 541004, China Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electrical Technology, Guilin 541004, China)

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004 [2]桂林电子科技大学广西高校数据分析与计算重点实验室,广西桂林541004

出　　处：《桂林电子科技大学学报》2016年第6期508-512,共5页Journal of Guilin University of Electronic Technology

基　　金：国家自然科学基金(11561015);广西自然科学基金(2016GXNSFFA380009)

摘　　要：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.

关 键 词：误差函数 Chebyshev级数 Clenshaw算法 IEEE浮点计算标准 

分 类 号：O241.1[理学—计算数学]