最小二乘三次拟合matlab
时间: 2023-11-26 10:48:58 浏览: 61
以下是使用MATLAB进行最小二乘三次拟合的步骤:
1.准备数据:将需要拟合的数据存储在一个矩阵中,其中第一列为自变量x,第二列为因变量y。
2.构建矩阵:根据最小二乘法的原理,需要构建一个矩阵A和一个向量b,其中A为一个3x3的矩阵,b为一个3x1的向量。具体构建方法如下:
```matlab
n = length(x);
A = [n, sum(x), sum(x.^2); sum(x), sum(x.^2), sum(x.^3); sum(x.^2), sum(x.^3), sum(x.^4)];
b = [sum(y); sum(x.*y); sum(x.^2.*y)];
```
3.求解系数:根据最小二乘法的公式,可以求解出系数向量c,其中c(1)为常数项,c(2)为x的系数,c(3)为x^2的系数,c(4)为x^3的系数。
```matlab
c = A\b;
```
4.绘制拟合曲线:根据求解出的系数向量c,可以绘制出拟合曲线。
```matlab
x_fit = linspace(min(x), max(x), 100);
y_fit = c(1) + c(2)*x_fit + c(3)*x_fit.^2 + c(4)*x_fit.^3;
plot(x_fit, y_fit);
```
完整代码如下:
```matlab
% 准备数据
x = [1, 2, 3, 4, 5];
y = [3, 6, 10, 15, 21];
% 构建矩阵
n = length(x);
A = [n, sum(x), sum(x.^2); sum(x), sum(x.^2), sum(x.^3); sum(x.^2), sum(x.^3), sum(x.^4)];
b = [sum(y); sum(x.*y); sum(x.^2.*y)];
% 求解系数
c = A\b;
% 绘制拟合曲线
x_fit = linspace(min(x), max(x), 100);
y_fit = c(1) + c(2)*x_fit + c(3)*x_fit.^2 + c(4)*x_fit.^3;
plot(x_fit, y_fit);
```