poly_fit.m

最小二乘实现多项式拟合

function coef = poly_fit(m,data)
%计算最小二乘法的系数方程
%输入参数：m为拟合多项式的次数，data为拟合数据，格式为二维列向量,第一列为自变量，第二列为因变量.
%输出参数：拟合多项式的系数行向量.
%调用关系：调用行向量内积函数inner_product(vector1,vector2)和高斯列主元消元法函数Gauss_solve(A).

x = data(:,1)';
y = data(:,2)';

for i = 1:(m+1)
    phi(i,:) = x.^(i-1);
end

for i = 1:(m+1)
    for j = i:(m+1)
        A(i,j) = inner_product(phi(i,:),phi(j,:));
        A(j,i) = A(i,j);
    end
    A(i,j+1) = inner_product(y,phi(i,:));
end
coef = Gauss_solve(A);