实数阶累加运算及其在GM(1,1)模型中的应用  

Real Order Accumulation and Its Use in GM(1,1) Mode

作　　者：吴正鹏[1] 张方红[1] 齐英剑[1] 李浩[1] 

机构地区：[1]中国传媒大学理学院,北京100024

出　　处：《应用泛函分析学报》2016年第4期422-427,共6页Acta Analysis Functionalis Applicata

摘　　要：本文考虑实数阶累加运算,从理论上证明了将所有实数阶累加运算看成一个集合,在其上定义普通数的加法与数乘运算后,其为交换群.分析表明先对原序列进行m阶累加,在新得到的序列中再进行1阶累加,等价于对原序列进行m+1阶累加,结果表明对原序列先进行m阶累加,然后再进行-m阶累加,序列就回到原始序列.同时s阶累减运算可看成-s阶累加运算,最后将分析结果用于GM(1,1)模型中,并进行误差分析.Based on the definition of real order accumulation, this paper has many interesting results. First, all of real order accumulations is a commutative group, according to ordinary addition of number and number-multiply. By the m order ac- cumulation of raw data and then I order accumulation, it is the same as the m ＋ 1 order accumulation, as m is equal to -rn, it went back to its original sequence. The accumulation of s order is the same as the inverse accumulation of -s order. At last, it was used in GM（1,1） model.

关 键 词：实数阶累加 GM(1 1)模型 误差分析 

分 类 号：N941[自然科学总论—系统科学]