Question

matlab拟合三次多项式 常数项为0 已知x,y对应的数据点，求y=184.56x+Ax^2+Bx^3,用什么方法可以拟合得出？

Answer 1

首先输入预定义x向量和y向量，元素个数必须相等。假设为：

>> x=[2.4,4,4.8,6,8];

>> y=[500 950 1200 1700 2800];

%代码如下：

Y=(y-184.56.*x)./(x.^2);%化为Y=A+Bx;

T=polyfit(x,Y,1);%将Y拟合成关于x的一次多项式

%输出A和B:

B=T(1)

A=T(2)

Y=A+B.*x;

y1=Y.*x.^2+184.56.*x;%y1=184.56x+Ax^2+Bx^3

plot(x,y);hold on;

plot(x,y1,'r');hold off; 

运行结果为：

B =

    1.9014

A =

    5.2002

追问

x=[0,0.005,0.01,0.03,0.06,0.08,0.10,0.13,0.15,0.18,0.22,0.25,0.28,0.31,0.34,0.37,0.39,0.41,0.44,0.46,0.48];
y=[0,0.16,2.10,5.43,10.65,16.14,20.67,27.32,32.62,40.60,52.05,61.86,70.52,80.50,90.80,100.67,110.44,120.05,130.51,140.24,151.41];
用上述数据做不出来啊

追答

因为x（1）=0，x的平方作分母时，分母为0，Y（1）非数，故得不到A,B
clear;clc;close all;
x=[0,0.005,0.01,0.03,0.06,0.08,0.10,0.13,0.15,0.18,0.22,0.25,0.28,0.31,0.34,0.37,0.39,0.41,0.44,0.46,0.48];
y=[0,0.16,2.10,5.43,10.65,16.14,20.67,27.32,32.62,40.60,52.05,61.86,70.52,80.50,90.80,100.67,110.44,120.05,130.51,140.24,151.41];
Y=(y-184.56.*x)./(x.^2+eps);%化为Y=A+Bx;
T=polyfit(x,Y,1);%将Y拟合成关于x的一次多项式
%输出A和B:
B=T(1)
A=T(2)
Y=A+B.*x;
y1=Y.*x.^2+184.56.*x;%y1=184.56x+Ax^2+Bx^3
plot(x,y);hold on;
plot(x,y1,'r');hold off;
运行结果为：
B =
1.2008e+004=12008
A =
-3.8451e+003=-3845.1
从图像上看，y不成x的四次函数。