How can I create a function that returns a function?

I'm tryng to create a function that returns to me the interpolation polynom of newton. This is the code:

function Y=newton(x,y)
syms X;
n=length(x);
b=zeros(n,n);
b(:,1)=y(:);
%finite difference matrix
for j=2:n
    for i=1:n-j+1
        b(i,j)= (b(i+1,j-1)-b(i,j-1))/(x(i+j-1)-x(i));
    end
end
%interpolation polynom
yint=b(1,1);
xt=1;
for j=1:n-1
    xt=xt*(X-x(j));
    yint=yint+b(1,j+1)*xt;
end
Y=yint

It's already working, but I want the output to be a function, so I can calculate it's value in any point, make graphics, etc.

[Vitor Pessoa]

function Y=newton(x,y)

syms X;

n=length(x);

b=zeros(n,n);

b(:,1)=y(:);

%finite difference matrix

for j=2:n

      for i=1:n-j+1

          b(i,j)= (b(i+1,j-1)-b(i,j-1))/(x(i+j-1)-x(i));
      end
  end
  %interpolation polynom
  yint=b(1,1);
  xt=1;
  for j=1:n-1
      xt=xt*(X-x(j));
      yint=yint+b(1,j+1)*xt;
  end
  Y=yint

Sorry, it was supposed to come out like this.

[Geoff Hayes]

Vitor - to properly format your code, highlight that text which is code and press the {}Code button.

Answer 1

[Walter Roberson]

Functions cannot return functions. Functions can return function handles, and functions can return symbolic expressions, and functions can return symbolic functions. The Y that you compute is already a symbolic expression; if you want to turn it into a function handle, use matlabFunction