% x1=0.13和x2=0.36的值
%x,y,n,x1,x2均可修改

% 拉格朗日

x=[0 0.1 0.2 0.3 0.4];
y=[0.5 0.5398 0.5793 0.6179 0.6554];
n=5;
for i=1:n
 l(i)=y(i);
  for j=1:n
   if i~=j
   l(i)=l(i)/(x(i)-x(j));
   end;   
  end;
end;

x1=0.13;
L1=0;
for i=1:n
  LL=1;
  for j=1:n   
   if i~=j
    LL=LL*(x1-x(j));
   end;
  end;
  LL=LL*l(i);
  L1=L1+LL;
end;
L1
x2=0.36;
L2=0;
for i=1:n
  LL=1;
  for j=1:n   
   if i~=j
    LL=LL*(x2-x(j));
   end;
  end;
  LL=LL*l(i);
  L2=L2+LL;
end;
L2





%牛頓

x=[0 0.1 0.2 0.3 0.4];
y=[0.5 0.5398 0.5793 0.6179 0.6554];
n=5;
nn=y;
for j=2:n
for i=n:-1:j
nn(i)=(nn(i)-nn(i-1))/(x(i)-x(i-j+1));
end
end 

x1=0.13;
N1=nn(1);
for i=2:n
  NN=1;
  for j=2:i
    NN=NN*(x1-x(j-1));
  end;
  NN=NN*nn(i);
  N1=N1+NN;
end;
N1
x2=0.36;
N2=nn(1);
for i=2:n
  NN=1;
  for j=2:i
    NN=NN*(x2-x(j-1));
  end;
  NN=NN*nn(i);
  N2=N2+NN;
end;
N2