get_poly_newton

function poly_newton = get_poly_newton(nodes,f_labels,x)
    table = get_table(nodes,f_labels);
    
    for i = 1:length(nodes)
      a(i) = table(i,i);
    end
    
    %P_n(x) = f_0 + f(x_0;x_1)(x-x_0) + f2(x_0;x_1;x_2)(x-x_0)(x-x_1) + ... + f(x_0;...;x_n)(x-x_0)(x-x_1)...(x-x_(n-1))
    for k = 1:length(x)
      res = 0;
      for i = 1:length(nodes)
        tmp = 1;
        for j = 1:i-1
          tmp = tmp*(x(k)-nodes(j));
        end
        res = res + tmp*a(i);
      end
      poly_newton(k) = res;
    end
end

function table_div_diff = get_table(nodes,f_labels)
  table_div_diff = zeros(length(nodes));
  
  for i = 1:length(nodes)
      table_div_diff(i,1) = f_labels(i);
  end
  
  for i = 2:length(nodes)
      for j = 2:length(nodes)
        if(i >=j)
          table_div_diff(i,j) = (table_div_diff(i,j-1) - table_div_diff(j-1,j-1))/(nodes(i) - nodes(j-1));
        end
      end
  end
end