Iterative refinement of Ax=b equation to have a residual equal to 0

I cant seem to figure out how to set up a for loop or while loop for find the least square solution to a problem when the residual is equal to zero. Any pointers?

clear all; close all;
% Given A, b, and ext 
A = [21,67,88,73;
    76,63,7,20;
    0,85,56,54;
    19.3,43,30.2,29.4];
b = [141;109;218;93.7];
ext = [-1;2;-3;4];
% LU factorization of A in single
[L1,U1] = lu(single(A));
% L1*U1*x=b ==> x=U1\(L1\b);
x1 = single(U1\(L1\b));
xs = double(x1);
save x1.dat xs -ascii
% norm of error
e1 = double(ext-xs);
e2 = double(norm(e1));
save error1.dat e2 -ascii
% residual
r1 = double(b-A*xs);
r2 = single(r1);
% solve Az=r ==> z=U1\(L1\r)
z = U1\(L1\r2);
x_s= xs + z;
% compute r and z as above until r=0

I'm not very good at while loops yet, but I am trying somewhere along the lines:

tol = 0;
while r4 < tol
    r3 = double(b-A*x_s);
    r4 = single(r3);
    z1 = U1\(L1\r4);
    x_s = x_s + z1;
end

[Youssef Khmou]

hi, i do not think you need loops, the sol is [-1 2-3 4] :

   X=inv(A'*A)*A'*b