310 MATLAB\'s qr command, which we introduced in Exercise 3.2.48, can be used to

Question

310 MATLAB's qr command, which we introduced in Exercise 3.2.48, can be used to compute QR decompositions of non-square matrices. Evercise 3.3.10 (e Try out the following commands, for example n=6 m-3 A-randn (n, m) norm (eye (n)-Q' *Q) norm (A-Q*R) In the interest of convenience, MATLAB returns Q in assembled form. Write a short MATLAB script (m-file) that solves least squares problems using the qr command. (The submatrix R can be accessed by writing R (1 :m, 1 :m) or R (1 :m, :), for example.) Use your script to work parts (a) and (b) of Exercise 3.3.9. This is not the simplest way to solve least squares problems using MATLAB. Recall from Exercise 3.1.5 that the command xAlb works as well. This gives you a simple way to check your work.

Explanation / Answer

or try this...[m,n] = size(A);
[Q,R,P] = qr(A);
c = Q'*b;
% The diagonal entries of R
%|R(1,1)| >= |R(2,2)| >= |R(3,3)| >= ..
% Find the smallest integer r
%|R(r+1,r+1)| < max(size(A))*eps*|R(1,1)|
tol = max(size(A))*eps*abs(R(1,1));
r = 1;
while ( abs(R(r+1,r+1)) >= tol & r < n ); r = r+1; end
y1 = R(1:r,1:r) c(1:r);
y2 = zeros(n-r,1);
x = P*[y1;y2];

Thanks in advance....

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