HermiteInterp.m

function f = HermiteInterp(x,y,y_1,x0)  
% 求已知数据点的向后差分牛顿插值多项式  
% 已知数据点的 x 坐标向量:x  
% 已知数据点的 y 坐标向量:y  
% 已知数据点的导数向量:y_1  
% 求得的Hermite插值多项式或x0处的插值:f  

syms t;  
f = 0.0;  
  
if(length(x) == length(y))  
    if(length(y) == length(y_1))  
        n = length(x);  
    else  
        disp('y和y的导数的维数不相等！');  
        return;  
    end  
else  
    disp('x和y的维数不相等！');  
    return;  
end  
for i = 1:n  
    h = 1.0;  
    a = 0.0;  
      
    %%计算hi和ai  
    for j = 1:n  
        if( j ~= i)  
            h = h*(t-x(j))^2/((x(i)-x(j))^2);  
            a = a + 1/(x(i)-x(j));  
        end  
    end  
      
    f = f + h*((x(i)-t)*(2*a*y(i)-y_1(i))+y(i));  
      
    if(i == n)  
        if(nargin == 4)  
            f = subs(f,'t',x0);  
        else  
            f = vpa(f,6);  
        end  
    end  
end