拟合实验数据的新方程——非整数幂多项式方程  

A modified equation for correlating experimental data——nonintegral power polynomial equation

作　　者：盛景云[1] 方维平[1] 王跃敏[1] 郑泉兴[1] 杨意泉[1] 

机构地区：[1]厦门大学化学系,福建厦门361005

出　　处：《计算机与应用化学》2004年第5期725-728,共4页Computers and Applied Chemistry

摘　　要：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。It is important to correlate experimental data into a continuous function in scientific research and technical development.Theequation mostly used for this purpose is polynomial:f(x)=c_0+c_1x+c_2x^2+…+c_nx^n.But the correlating results of this polynomialare sometimes undesirable.In this paper,a modified equation for this usage is proposed:g(x)=c_0+c_1x^a+…+c+x x^(ka)+c_(k+1)x^(k+1)b+…+c_n x^(nb),where a and b are parameters and c_i(i=0,1,2,…n)are undetermined coefficients.When this new equation is used forcorrelating different kinds of experimental data(curve),smaller errors will always be obtained in comparison with the normal polynomi-al f(x).

关 键 词：拟合 实验曲线 实验数据 方程 多项式 

分 类 号：O657.31[理学—分析化学]