matlab experiment - Lagrange interpolation Runge (Runge) phenomenon

Remember a math homework
learn to use the Lagrange polynomial

n=15;  %5,10,15插值点数
syms t;

x = linspace(-5,5,n);
y=f(x);
for i=1:n
L(i)=Lagrange(x,n,i,t);
end
LN=sum(y.*L);
t=-5:0.01:5;
y0=5./(1+t.^2);
 plot(t,y0);
 hold on;
 ezplot(LN,t);
 a=strcat('实验一：',num2str(n),'次插值');
 title(a);
 legend('原函数','插值函数');

function fi=Lagrange(x,n,i,t)

fu=1;
fd=1;

for  j=1:n                      %循环计算 
         if i~=j
             fu=fu.*(t-x(j));
             fd=fd.*(x(i)-x(j));
         end
end
fi=fu/fd;
end
  
function y=f(x)
y=5./(1+x.^2);
end