利用公式ζ(2)=π~2/6快速计算圆周率  

Fast Algorithms for Ratio of the Circumference of a Cycle to Its Diameter by Using Formula ζ(2)=π~2/6

作　　者：唐建国[1] 

机构地区：[1]湖南科技学院数学与计算科学系,湖南永州425006

出　　处：《大学数学》2006年第4期122-126,共5页College Mathematics

基　　金：湖南省自然科学基金项目(03JJY3014)资助

摘　　要：在等式π2/6=ζ(2)中将1/l2拆分为一系列以若干连续正整数之积为分母的分数之和,利用这些正分数特有的性质,给出了级数ζ(2)第n项以后各项之和的高精度快速算法,其误差小于(n-1)!n!高精度π值,误差显示计算精度达到1.0E-3023时仅需20000个运算量.In equality ξ（2）=π^2/6 we decompose 1/l^2 into the sum of a series of fractions with denominator composed of product of continuously positive integer. Fast high accuracy algorithms for the sum of all terms after the n-th one of the series ξ（2） are constructed by using the properties of these fractions, which only need 4n=3 operations and the error is less than （n-1）!n /（n＋1）^2（n＋2）· （2n）! .Based on this, the high accuracy value of π is obtained by using the fast algorithm for arithmetic square root. Numerical results show that only 20000 operations are needed as the accurancy reach 1.0E--3023 .

关 键 词：π值高精度快速算法 连续正整数之积的倒数 运算量 误差 

分 类 号：O241[理学—计算数学]