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将实验数据拟合成方程在科学研究和工程计算上具有十分重要的作用。目前,拟合实验数据最常用的是整数幂多项式f(x)=c_0+c_1x+c_2x~2+…+c_nx~n,但是用此多项式拟合各类数据时有时误差较大。本文提出一个新方程,即双系列非整数幂多项式g(x)=c_0+c_1x~0+…+c_kx~(ka)+c_(k+1)x~[(k+1)b]+…+c_nx~(nb),式中a,b为参数,c_i(i=0,1,2,…,n)为待定系数。在拟合各类实验数据时,新方程总是优于整数幂多项式。
Fitting experimental data into equations plays a very important role in scientific research and engineering calculation. At present, the polynomial f (x) = c_0 + c_1x + c_2x ~ 2 + ... + c_nx ~ n which is most commonly used to fit experimental data is fit. However, when polynomials are used to fit various types of data, errors sometimes occur. In this paper, we propose a new equation that is a series of non-integer power polynomials of the series g (x) = c_0 + c_1x ~ 0 + ... + c_kx ~ (ka) + c_ (k + 1) x ~ [(k + 1) b] + + c_nx ~ (nb), where a and b are parameters and c_i (i = 0, 1, 2, ..., n) is the undetermined coefficient. When fitting various experimental data, the new equation is always better than the integer power polynomial.