approx_func_plot(5,3);
approx_func_plot(5,5);
approx_func_plot(5,10);
approx_func_plot(5,20);

function [Fi] = approx_func_plot(n,k)
Fi = zeros(n,k);
f = @(x) sqrt(1-x^2)*exp(x);
   for i=1:n
       x(i) = -1 + 2*(i-1)/(n-1);
       y(i) = f(x(i));
   end

   for i=1:k
       xk(i) = -1 + 2*(i-1)/(k-1);
   end


   for j=1:k
       for i=1:n
           Fi(i,j) = sinc(x(i) - xk(j));
       end
   end


   y = y';
   A = Fi'*Fi;
   b = Fi'*y;

   p = A\b;

   x = linspace(-1,1,100);
   for i=1:100
       y_100(i) = f(x(i));
   end

   tmp2 = 0;

   for i=1:100                 % CREATING APPROX FUNCTION OUTOUT
       for j=1:k
           tmp = p(j)*sinc(x(i)-xk(j));
           tmp2 = tmp2 + tmp;
       end
       fapp(i) = tmp2;
       tmp2 = 0;
   end

   f4 = figure;
   figure(f4);
   plot(x,fapp, x, y_100);
   legend('approximated', 'real function');
   title(['Approximated function for n= ' num2str(n) ' k= ' num2str(k)]);
   xlabel('x');
   ylabel('y');
end