同符号数相加“大数吃小数”的界限:数值试验  

On bound of a large number annihilating a small number in addition operation of two numbers with same sign: numerical experiment

作　　者：曹靖[1,2,3] 李建平[1,2] 

机构地区：[1]中国科学院大气物理研究所,北京100029 [2]中国科学院研究生院,北京100029 [3]天津理工大学理学院,天津300384

出　　处：《天津师范大学学报（自然科学版）》2014年第2期16-18,共3页Journal of Tianjin Normal University：Natural Science Edition

基　　金：国家自然科学基金资助项目(41375110;41175069);中国科学院大气物理研究所大气科学和地球流体力学数值模拟国家重点实验室(LASG)2012年度开放课题

摘　　要：利用大量数值试验,得出机器单双精度下关于两同符号数相加时"大数吃小数"界限的数据.对试验数据进行分段线性拟合,给出"大数吃小数"界限的近似公式,与试验数据比较表明近似公式具有良好的估计效果,可为单双精度下避免"大数吃小数"现象提供可靠的依据.进一步,将机器单双精度的结果推广至任意机器精度,得到的结论可方便应用于实际的数值运算中.Through a lot of numerical experiments, the data of the bounds of a large number annihilating a small number in addition operation of two numbers with same sign under single and double machine precisions are obtained. By analyz-ing the experimental results, piecewise linear approximations of the bounds have been established. The approximate func-tions show good performances when comparing with the exact results in numerical experiments. Moreover, based on the results under single and double machine precisions, generalized approximate function for any given machine precisions has been deduced, which can be conveniently applied in practical numerical computations.

关 键 词：“大数吃小数” 分段线性拟合 机器精度 

分 类 号：O246[理学—计算数学]